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CURRICULUM VITAE
Name : SUBHASHISH BANERJEE
Sex : Male
Address for Correspondence:
Subhashish Banerjee
Indian Institute of Technology Jodhpur,
NH 62, Nagaur Road , Karwar, Jodhpur-342037
Email : [email protected]; [email protected].
Homepage: http://home.iitj.ac.in/ subhashish/
1. Academic Records:
(a) Bachelor of Engineering (B.E.) 1996, Delhi College of Engineering, Delhi Univer-
sity, New Delhi, India.
(b) Ph.D obtained in August 2003, School of Physical Sciences, J.N.U., New Delhi,
India.
Thesis Title:
“Study of Dynamics of Open Quantum Systems using the Functional Integral Approach.”
Thesis Supervisor:
Prof. R. Ghosh, School of Physical Sciences, J.N.U.
Research and Teaching Experience:
1. Postdoctoral Position:
(a) Postdoctoral Position: From February 2004 till April 2005 in Fachbereich
Physik, Kaiserslautern (Germany). Postdoctral Supervisor: Prof. Dr. Joachim
Kupsch.
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(b) Postdoctoral Visitor: June, July 2005 in Centre for High Energy Physics
(CHEP), Indian Institute of Science (IISc), Bangalore (India).
(c) Postdoctoral Position: From September 2005 to July 2008, in the Theoretical
Physics Group, Raman Research Institute, Bangalore (India).
2. Faculty Position:
(a) From August 2008-March 2010 at Chennai Mathematical Institute, Siruseri, Chen-
nai, India: Visiting Fellow;
(b) From April 2010- June 2010 at Chennai Mathematical Institute, Siruseri, Chennai,
India: Asst. Prof.;
(c) From July 2010 at Indian Institute of Technology Rajasthan, Jodhpur, India:
Asst. Prof.
3. Teaching Experience:
(a) Course instructor at Indian Institute of Technology Rajasthan:
i. Physics-I (Ist Semester, Undergraduate B.E.): This course consists of the
elements of electrostatics, electrodynamics as well as the nature of these laws
in, say, a dielectric medium. Then the elements of special theory of relativity
are covered, followed by an introduction to quantum mechanics. The idea is
to provide the students with a basic understanding of the need for quantum
mechanics, at an early stage. Thus the basic idea of wave-particle duality
is stressed and is supplemented with discussions of the photoelectric and
Compton effect.
ii. Physics-II (IInd Semester, Undergraduate B.E.): This course deals with
an amalgamation of statistical mechanics and solid state physics. The ba-
sic ideas of X-ray diffraction are discussed followed by some basic concepts
in equilibrium statistical mechanics, with a stress on the various statistical
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distributions existing in nature; the emphasis being on the Fermi-Dirac dis-
tributions. This is followed by a discussion of free Fermi gas, band theory. All
this is then put to use to understand metals, semi-conductors and insulators.
In semi-conductors, the p-n junction is discussed thoroughly, and is used to
discuss devices such as Zener diodes, transistors, photovoltaic diodes or solar
cells.
iii. Undergraduate Physics Laboratory (Ist Semester, Undergraduate B.E.):
Involved in the running of the undergraduate physics laboratory in the first
semester: which involved experiments related to mechanics, electromagnetism,
optics. Some of the experiments performed were:
Stationary waves in string; verification of Newton’s Second Law; moment
of inertia of a bicycle wheel; determination of e/m ration; interference and
diffraction of light; refractive index of a prism; magnetic forces on wires;
Faraday’s law of induction.
iv. Physics-III (IIIrd Semester, Undergraduate B.E.): Developed and taught
the course Physics-III, containing Newtonian Mechanics, Rotational Dynam-
ics, Special Theory of Relativity, Motion Under Central Forces, and an In-
troduction to Non-Linear Dynamics where concepts such as Fixed points,
stability; determination of fixed points; limit cycles; periodic conditions and
linear maps; chaotic motion and non-linear maps are discussed.
v. Quantum Mechanics and Its Applications (IVth Semester, Undergradu-
ate B.E.): introducing quantum mechanics to undergraduate students. Basic
experiments, concepts and a brief glimpse of some of its modern applications
such as quantum optics and information, nuclear and particle physics.
vi. Quantum Mechanics Laboratory (IVth Semester, Undergraduate B.E.):
basic ideas of quantum mechanics illustrated via the Franck Hertz experiment,
e/m ratio, B−H curve, photoelectric effect, band gap of semiconductors and
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optics experiments such as diffraction grating.
vii. Nature and Properties of Materials Laboratory (IInd Semester, Un-
dergraduate B.E.):
This lab course aims at providing a glimpse to the students of various aspects
of material properties of systems, such as thermal, optical and mechanical
properties, some of which they have already studies in their Physics-II course.
viii. Introduction to Quantum Computation and Information: designed
and taught this course, consisting of an Introduction to Quantum Mechanics,
Quantum Computation, Classical Information and Communication, Quan-
tum Information, Entanglement, Quantum Communication and some appli-
cations, such as Quantum copying, deletionand quantum cryptography.
ix. Introduction to System Science and Dynamics: course on Systems
Science for M.Tech. and Ph.D. students. We highlight the ubiquitousness of
the systems philosophy, by applications to concrete systems such as spring
systems. These systems are prototypes of systems modelling, as they occur in
the physical sciences as well as in numerous engineering applications, such as
in Electric Circuit Theory. We then discuss the fundamental concepts of self-
organization and synergetics with examples drawn from problems in physics,
biology and sociology.
x. Introduction to Cryptography and Coding: Here we introduce the ba-
sic concepts of cryptography and coding, classical as well as quantum. This
is a course for Post Graduate Students as well as interested final year under-
graduate students.
xi. Information Theory and Probability: for Postgraduate students;
xii. Relativistic Quantum Mechanics: Quantum mechanics in the relativistic
regime, for graduate students. The course consists of discussions of relativistic
wave equations, Maxwell, Klein-Gordan and Dirac. Also discussed are the
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concepts of symmetry in the relativistic regime.
xiii. Quantum Field Theory: an introductory course on quantum field theory
for graduate students. The course deals with Noether’s theorem, canonical
quantization of free and interacting field theories such as Klein-Gordan, Dirac
and Maxwell theory.
xiv. Quantum Mechanics: an introduction of quantum mechanics to MSc (Mas-
ters in Science) students. The course covers postulates of quantum mechanics,
uncertainty principle, time-independent perturbation theory, harmonic oscil-
lators, angular momentum and the Hydrogen atom.
xv. Statistical Mechanics: basic thermodynamics and statistical mechanics for
MSc students;
xvi. Atomic and Nuclear Physics: introduction to atomic and nuclear physics
for MSc students;
xvii. Electrodynamics: Basic electrodynamics, with an introduction to relativis-
tic effects and optics, for masters students (MSc Physics);
xviii. Basic Physics: an elementary introduction to modern aspects of physics
such as quantum mechanics, atomic and nuclear physics, special relativity,
lasers and superconductivity to BSc (Bachelor of Science) students at NLU
(National Law University) Jodhpur, India.
(b) Course instructor at Chennai Mathematical Institute for:
i. Newtonian Mechanics: This course deals with Newtonian mechanics and
its consequences. The emphasis here is in an appreciation of the inherent
conservation laws that form the basis of the phenomena studied. Also, wher-
ever possible, experiments are discussed. For e.g., the beautiful experiment
performed by I. Estermann et al.: Phys. Rev. A: 71, 238 (1947), to test the
theoretical velocity distribution of atoms at a given temperature making use
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of Newtonian mechanics to the free fall of individual atoms;
ii. Statistical Mechanics-I: Thermodynamics: Thermodynamics is a re-
markably successful theory about the macroscopic world. This course deals
with spelling out the phenomenological origin of thermodynamics, in partic-
ular equilibrium thermodynamics and studying its various consequences;
iii. Statistical Mechanics-II: Here we deal with the microscopic theory un-
derlying the macroscopic manifestations of thermodynamics. This course is
about equilibrium phenomena. The concept of ensembles in classical statis-
tical mechanics is developed in length and the program is carried forward
to quantum statistical mechanics. This is then applied to a number of phe-
nomena such as magnetism, black body radiation, theory of solids and Bose-
Einstein condensation.
iv. Statistical Mechanics-III: Ising model, phase transition, elements of non-
equilibrium statistical mechanics.
(c) Teaching experience during PhD and Post-Doctoral period:
i. Teaching assistant for courses in electromagnetic theory, quantum mechanics
and quantum field theory in J.N.U., New Delhi.
ii. Teaching assistant for courses in quantum mechanics and statistical mechanics
in Fachbereich Physik, Kaiserslautern.
Conferences Attended:
1. International Conference on “Recent Developments in Theoretical Physics”, T.I.F.R.,
Mumbai, January 1999.
2. International Conference on “Foundations of Quantum Mechanics and Quantum Op-
tics”, S. N. Bose Centre, Calcutta, January 2000.
3. SERC School 2000 on “Field Theories in Condensed Matter Systems”, M.R.I. Alla-
habad, February 2000.
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4. International Symposium on “Entanglement, Information and Noise”, June 14-20,
2004 in Krzyzowa, Poland. Presented a poster on “Decoherence and Dissipation of an Open
Quantum System with a Squeezed and Frequency-Modulated heat bath”.
5. 330th WE-Heraeus Seminar on “Controlling Decoherence”, July 26-28, 2004 in Bad
Honnef, Germany. Presented a poster on “The effect of Squeezing of the Bath on the
Decoherence and Dissipation properties of an Open Quantum System”.
6. D.I.C.E. 2004 on “From Decoherence and Emergent Classicality to Emergent Quantum
Mechanics”, September 1-4, 2004 in (Castello di) Piombino, Italy.
7. Non-Equilibrium Phenomena: Tenth Discussion Meeting in a Frontier Area of Re-
search; January 2006, Bangalore, India.
8. Entanglement in Quantum Condensed Matter Systems: 17-29 November, 2008, at
Institute of Mathematical Sciences, Chennai, India.
9. “International Program on Quantum Information (IPQI)” held at Institute of Physics
(IOP), Bhubaneswar, Orissa, India: January 4th-30th, 2010.
10. “ International Conference on Quantum Optics and Quantum Computing (ICQOQC-
11): March 24-26, 2011; organized by the Department of Physics and Materials Science and
Engineering, Jaypee Institute of Information Technology, Noida, India.
11. “International Program on Quantum Information (IPQI) 2011” held at Institute of
Physics (IOP), Bhubaneswar, Orissa, India from December 13th-22nd, 2011.
12. “International Workshop on Quantum Information (IWQI) 2012” held at Harish
Chandra Research Institute (HRI), Allahabad, India from January 20th-26th, 2012.
13. “8th Nalanda Dialog on Science and Philosophy” held at Nava Nalanda Mahavihara,
Nalanda, Bihar from January 21-24, 2013.
Seminars Presented at:
1. School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India.
2. University of Kaiserslautern, Germany.
3. University of Augsburg, Germany.
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4. University of Cologne, Germany.
5. Centre for High Energy Physics, Indian Institute of Science, Bangalore, India.
6. Indian Institute of Astrophysics, Bangalore, India.
7. Raman Research Institute, Bangalore, India.
8. Indian Institute of Technology, Kanpur, India.
9. Chennai Mathematical Institute, Chennai, India.
10. Institute of Mathematical Sciences, Chennai, India.
11. Institute of Physics, Bhubaneswar, India.
12. Harish-Chandra Research Institute, Allahabad, India.
13. Indian Statistical Institute (ISI), Kolkata.
14. Cultivation of Science, Kolkata.
15. Department of Physics and Materials Science and Engineering, Jaypee Institute of
Information Technology, Noida, India.
16. University of Freiburg, Freiburg, Germany (June, 2017). Title of Talk “Aspects Of
Non-Markovianity in Quantum Walks”.
17. Institute for Theoretical Physics, TU Wein (June, 2017). Title of Talk “Aspects Of
Non-Markovianity in Quantum Walks”.
18. University of Technology of Troyes (UTT), France (June, 2017). Title of Talk “An
Invitation to Open Quantum Systems and Quantum Cryptography”.
Outreach:
1. Was an active participant in: (a) Workshop on Systems Science - Complex Networks
and Applications, May 07-09, 2012;
(b) International Workshop on Quantum Biology, January 25-27, 2013;
(c) International Workshop on Computational Materials Design and Engineering, Febru-
ary 8-10, 2013;
held at Indian Institute of Technology Jodhpur.
2. Convener of International Meet on Quantum Correlations and Logic, Language and
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Set Theory 2013, at Indian Institute of Technology Jodhpur from December 9 to 14, 2013.
3. Course Coordinator of GIAN programme 171009M01 Topological Solitons and their
Applications, from December 10-15, 2018 at IIT Jodhpur. External faculty was Prof. Richard
MacKenzie of University of Montreal, Canada.
4. Invited speaker to fifteen international conferences on Quantum Information.
5. Invited speaker to the 8th Nalanda Dialog on Science and Philosophy held at Nava
Nalanda Mahavihara, Nalanda, Bihar, India from January 21-24, 2013.
6. Keynote speaker at the “One-Day Workshop on Quantum Communications” at
Malviya National Institute of Technology (MNIT) Jaipur in September 2016.
7. As the first Head of the Physics Department at IIT Jodhpur, helped to develop the
MSc Physics program introduced in July 2015. This involved, among other things, devel-
opment of the courses and getting them approved from an external committee of senior
Physicsts from the various IITs and TIFR (Mumbai).
Invited Speaker at National and International Conferences:
1. Invited speaker to the “Symposium on Quantum Information”, 16-17 March, 2007 at
School of Physical Sciences, Jawaharlal Nehru University, N. Delhi. Title of talk: “Deco-
herence without dissipation and its applications to Quantum Computation”.
2. Invited speaker in “Entanglement in Quantum Condensed Matter Systems” : 17-
29 November, 2008 at Institute of Mathematical Sciences, Chennai, India. Title of talk:
“Open Quantum Systems”.
3. Invited speaker in “International Program on Quantum Information (IPQI)” held at
Institute of Physics (IOP), Bhubaneswar, Orissa, India from January 4th-30th, 2010. Title
of talk: “Dynamics of Entanglement in Open Quantum Systems”.
4. Invited speaker in “ International Conference on Quantum Optics and Quantum
Computing (ICQOQC-11): March 24-26, 2011; organized by the Department of Physics
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and Materials Science and Engineering, Jaypee Institute of Information Technology, Noida,
India. Title of talk: “Effect of Control Procedures on Entanglement Evolution in Open
Quantum Systems”.
5. Invited speaker in “International Program on Quantum Information (IPQI) 2011”
held at Institute of Physics (IOP), Bhubaneswar, Orissa, India from December 13th-22nd,
2011. Title of talk: “Dynamics of Quantum Correlations in Open Quantum Systems”.
6. Invited speaker in “International Workshop on Quantum Information (IWQI) 2012”
held at Harish Chandra Research Institute (HRI), Allahabad, India from January 20th-26th,
2012. Title of talk: “Aspects of Open Quantum Systems in Quantum Information”.
7. Invited speaker in “8th Nalanda Dialog on Science and Philosophy” held at Nava
Nalanda Mahavihara, Nalanda, Bihar from January 21-24, 2013.
8. Invited speaker in “International Workshop in Optical Quantum Information” Septem-
ber 01-2, 2013; organized by the Department of Physics and Materials Science and Engineer-
ing, Jaypee Institute of Information Technology, Noida, India. Title of talk: “A Journey
from Quantum Optics to Quantum Information”.
9. Invited speaker in “Meeting on Quantum Information Processing and Applications
(QIPA-2013)”: December 02-08, 2013 at Harish-Chandra Research Institute (HRI), Alla-
habad, India. Title of talk: “Quantum Information: From the perspective of Quantum
Optics”.
10. Invited speaker in “National Conference on Quantum Correlations: Foundations and
Applications” from March 04-05, 2014; organized by Department of Physics, Vidyasagar
College for Women, Kolkata along with Physics and Applied Mathematics Unit, Indian
Statistical Institute, Kolkata. Title of talk: “An Invitation to Open Quantum Systems
Applied to Quantum Information”.
11. Invited speaker in “School and Discussion Meeting Frontiers In Light-Matter Inter-
actions” December 08-22, 2014 at Cultivation of Science, Kolkata and organized by ICTS,
Bangalore. Title of talk: “An Invitation to Open Quantum Systems: A Density Matrix
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Approach”.
12. Invited speaker in “International Conference on Quantum Foundations (ICQF15)”
November 30- December 04, 2015 organized by NIT, Patna. Title of talk: “Quasidistribu-
tions and Tomograms in Open Quantum Systems”.
13. Invited speaker in “Meeting on Quantum Information Processing and Applications
(QIPA-2015)” December 07-13, 2015 at Harish-Chandra Research Institute (HRI), Alla-
habad, India. Title of talk: “Open Quantum Systems and Quantum Information in Rela-
tivistic and Sub-atomic Systems”.
14. Invited speaker in “International Conference on Quantum Foundations (ICQF17)”
December 04- 09, 2017, organized by NIT, Patna. Title of talk: “Aspects Of NonMarko-
vianity In Quantum Walks”.
15. Invited speaker in “International Symposium on New Frontiers in Quantum Cor-
relations (ISNFQC18)”, January 29- February 03, 2018, organized by S N Bose Centre for
Fundamental Sciences, Kolkata. Title of talk: “Open Quantum Systems and Quantum
Information in Sub-atomic Systems”.
16. Invited speaker in “Workshop on Quantum Metrology and Open Quantum Systems”,
August 26-31, 2018, Kodaikanal Solar Observatory, organized by IMSc, Chennai. Title of
talk: “Open Quantum Systems and Quantum Information in Relativistic and Sub-atomic
Systems.”
Invited Reviewer:
1. Invited reviewer for Mathematical Reviews (MR) (a division of the American Mathe-
matical Society). Reviewed the papers:
a. “Dynamics of pairwise entanglement between two Tavis-Cummings atoms” by J-L.
Guo and H-S. Song. Journal ref.: Jr. of Phys. A: Math. Theor. 41, 085302 (2008);
b. “ Environment-invariant measure of distance between evolutions of an open quantum
system” by M. D. Grace; J. Dominy; R. L. Kosut; C. Brif and H. Rabitz. Journal ref.: New
Journal of Physics 12, 015001 (2010); Review Number: MR2581170;
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c. “ Maps for general open quantum systems and a theory of linear quantum error
correction” by A. Shabani and D. A. Lidar. Journal Ref.: Phys. Rev. A 80, 012309 (2009);
Review Number: MR2580789;
d. “Coherent states for a polynomial su(1, 1) algebra and a conditionally solvable system”
by M. Sadiq; A. Inomata; G. Junker. Journal Ref.: J. Phys. A 42, 365210 (2009); Review
Number: MR2534518;
e. “A Quantum Coupler and the Harmonic Oscillator Interacting with a Reservoir:
Defining the Relative Phase Gate” by P. C. Garcia Quijas and L. M. AreValo Aguilar.
Journal Ref.: Quantum Information and Computation 10 190 (2010); Review Number:
MR2649358;
f. “Position-dependent mass oscillators and coherent states” by S. Cruz y Cruz; O.
Rosas-Ortiz. Journal Ref.: J. Phys. A 42, 185205 (2009); Review Number: MR2591199;
g. “The rotating-wave approximation: consistency and applicability from an open quan-
tum system analysis” by C. Fleming; N. I. Cummings; C. Anastopoulos and B L Hu. Journal
Ref.: J. Phys. A 43, 405304 (2010); Review Number: MR2740391.
h. “Complex WKB evolution of Markovian Open Systems” by O. Brodier and A. M.
Ozorio de Almeida. Journal Ref.: J. Phys. A:Math. Theor. 43 505308, (2010); Review
Number: MR2725563.
i. “Stabilizing Quantum States by Constructive Design of Open Quantum Dynamics” by
F. Ticozzi; S. G. Schirmer and X. Wang. Journal Ref.: IEEE Transcations On Automatic
Control 55 2901 (2010); Review Number: MR2767162.
j. “Quantum Memories as Open Systems ” by Robert Alicki. Journal Ref.: Mathematical
Horizons for Quantum Physics, 97-108, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ.
Singap., 20, World Sci. Publ., Hackensack, NJ, 2010; Review Number: MR2731890.
k. “Open Quantum Systems In Non-Inertial Frames” by S. Khan; M. K. Khan. Journal
Ref.: J. Phys. A 44 045305 (2011); Review Number: MR2754724.
l. “Quantum Open Systems with Time-Dependent Control” by Robert Alicki. Journal
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Ref.: Lect. Notes Phys. 787, 79 (2010); Review Number: MR2762153.
m. “ Exact solutions for a family of spin-boson systems” by Yuan-Harng Lee, Jon
Links and Yao-Zhong Zhang, Journal Ref: Nonlinearity 24 1975 (2011); Review Number:
MR2805589.
n. “Shell Model for Open Quantum Systems” by M. Ploszajczak and J. Okolowicz.
Journal Ref.: Int J Theor Phys. 50 1097 (2011); Review Number: MR2780950.
o. “ Resonant-state Expansion of the Green’s Function of Open Quantum Systems” by
Naomichi Hatano and Gonzalo Ordonez. Journal Reference: Int J Theor Phys. 50 1105
(2011); Review Number: MR2780951.
p. “A new kind of geometric phases in open quantum systems and higher gauge theory”
by David Viennot and Jose Lages. Journal Reference: J. Phys. A: Math. Theor. 44 365301
(2011); Review Number: MR2826547.
q. “New Approach for Solving the Lindblad Equation of the Density Operator for a
Harmonic Oscillator Interacting with an Electromagnetic Field” by Jun Zhou, Hong-Yi Fan
and Jun Song. Journal Reference: Int. J. Thor. Phys. 50 3149 (2011); Review Number:
MR2833198.
r. “Volume fractions of the kinematic ‘near-critical’ sets of the quantum ensemble control
landscape” by Jason Dominy and Herschel Rabitz. Journal Reference: J. Phys. A: Math.
Theor. 44 255302 (2011); Review Number: MR2800875.
s. “ Wigner Function of a Special Type of Squeezed Coherent State” by Jun Song; Hong-
yi Fan. Journal Reference:Int J. Theor. Phys. 51 229 (2012); Review Number: MR2870433.
t. “Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator
and their Entanglement” by Yusef MALEKI. Journal Reference: SIGMA 7 084 (2011);
Review Number: MR2861192.
u. “Non-Markovian dynamics and entanglement of two-level atoms in a common field”
by C H Fleming; N I Cummings; Charis Anastopoulos; B L Hu. Journal Reference: J. Phys.
A: Math. Theor. 45 065301 (2012); Review Number: MR2881061.
13
v. “Atomic Coherent States and Sphere Maps” by Robert Gilmore. Journal Reference:
J. Phys. A:Math. Theor. 45 244024 (2012); Review Number: MR2930519.
w. “ Gazeau-Kaluder Cat States” by Jerzy Dajka and Jerzy Luczka. Journal Reference:
J. Phys. A:Math. Theor. 45 244006 (2012); Review Number: MR2930501.
x. “Effective Methods In Investigation Of Irreducible Quantum Operations” by Andrzej
Jamiolkowski. Journal Reference: International J. of Geometric Methods in Mod. Phys. 9
1260014 (2012); Review Number: MR2913152.
2. Invited reviewer for Pramana; J. of Stat. Phys.; J. Phys. A; J. Phys. B; Physica A;
Quantum Information and Computation (QIC) and Quantum Information and Processing
(QIP); Phys. Rev. A, Phys. Rev. D.
Brief Summary of Research Work:
I have been involved in studies in quantum statistical mechanics. In particular, the major
theme of my work is to show how The theory of Open Quantum Systems provides a
common umbrella to understand quantum optics, quantum information processing, quantum
computing, quantum cryptography, relativistic quantum mechanics, particle physics and
the foundations of quantum mechanics. The theory of open quantum systems addresses
the problems of damping and dephasing in quantum systems by its assertion that all real
systems of interest are in fact ‘open’ systems, each surrounded by its environment. The recent
upsurge of interest in the problem of open quantum systems is because of the spectacular
progress in manipulation of quantum states of matter (atoms, or bosonic or fermionic gases
or molecules), encoding, transmission and processing of quantum information, for all of
which understanding and control of the environmental impact are essential. The Nobel
Prize for 2012 was awarded to D. J. Wineland and S. Haroche for experimental justifications
of quantum coherence and its decay in realistic scenarios. In a number of my works involving
the application of open system ideas to quantum information and quantum optics, I have
made use of the experimental results of Wineland and Haroche.
The projects I have been involved in range from the fundamental aspects of quantum
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statistical mechanics to the mathematical physics aspects of canonical transformations in
Fock space. Over the last few years I have been developing a graphical representation
of quantum mechanics. I have also been involved in studies in quantum optics including
the study of quantum nondemolition systems and those directed towards the control over
decoherence in open quantum systems, having relevance to, for example, quantum computers.
I have used open system ideas to quantum random walk which is studied from the point
of view of the interplay between symmetries and noise. I have also been involved in work
related to phases in open quantum systems and have applied open system ideas to quantum
computation.
A broad theme that I have started work on is the connection between geometry and
statistical mechanics. In a study of complex systems use is made of Renyi and Tsallis
entropies, generalizations of the well known Shannon entropy. The entropic formulation
of statistical mechanics is the ingredient which enables a connection between statistical
mechanics and the corresponding Riemannian geometry. An investigation into the most
general meaning of intrinsic Riemannian geometry for complex systems is made by studying
the Ricci curvature of a number of physical situations modeled by Renyi and Tsallis entropies.
Also, a two-parameter generalization of Renyi and Tsallis entropies, along with a family of
other entropies, are proposed using a generalized difference operation bringing out their
connection to quantum groups.
I am also interested in the field of nonlinear dynamics. In this context, I have been
involved in some works on low dimesional maps such as the logistic map which have been q-
deformed. I have been working towards reaching a coherent understanding of non-Markovian
phenomena. Ideas from non-Markovian physics find a rich breeding ground for investigations
into quantum thermodynamics and also find a number of practical applications.
I have become interested recently in Flavor Physics that explores the deviations of pre-
dictions from the Standard Model. A major thrust in this direction is the probing of the
foundations of physics at the subatomic level. This can yield a number of surprises. Thus,
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on one hand, a study of quantum correlations in neutral mesons reveals features not seen
in stable quantum systems and on the other hand, the use of open system ideas on these
systems leads to predictions that suggest a rethinking of the interpretation of important
observables in particle physics and also suggests background effects which could be possible
signatures of quantum gravity.
I give below a brief summary of the work done as well as of the work in progress.
1 Open quantum systems
• The dynamics of an open quantum system exhibiting quantum Brownian motion is
analyzed when the coupling between the system and its environment is nonlinear, and
the system and the reservoir are initially correlated. For couplings quadratic in the en-
vironment variables, the influence functional for the system is obtained perturbatively
up to second order in the coupling constant, and then the propagator is explicitly evalu-
ated when the particle is under the influence of a harmonic potential and an additional
anharmonic potential, the so-called Washboard potential. As an application of the
propagator, the master equation and the Wigner equation are obtained for the quan-
tum Brownian particle moving in a harmonic potential for the generalized correlated
initial condition, and then for the specific case of the simplified ’thermal’ initial condi-
tion. The system is shown to obey the corresponding fluctuation-dissipation theorem
(ref. [3]).
• The effect of squeezing and modulation on the decoherence and dissipation properties
of an open quantum system are studied. The functional integral formalism is used
to provide a unified treatment of the effect of squeezing of the bath and frequency
modulation of the system bath coupling on the decoherence and dissipation properties
of a quantum open system. The system chosen is a standard one consisting of a particle
in a harmonic oscillator potential interacting with a bath of harmonic oscillators by a
coupling of the position-position kind. Using an ohmic bath and the high temperature
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limit the coefficients of the master equation describing dissipation and decoherence are
obtained and analyzed (ref. [4]).
• Use is made of the study (ref. [5]) for some applications of canonical transformations.
It is shown that the single-mode and the n-mode squeezing operators are elements of
the group of canonical transformations. An application is made, in the context of open
quantum systems, by studying the effect of squeezing of the bath on the decoherence
properties of the system. Two cases are analyzed. In the first case the bath consists
of a massless bosonic field with the bath reference states being the squeezed vacuum
states and squeezed thermal states while in the second case a system consisting of a
harmonic oscillator interacting with a bath of harmonic oscillators is analyzed with the
bath being initially in a squeezed thermal state (ref. [6]).
• A study is made of open quantum systems where the coupling between the system and
its environment is of a quantum nondmolition (QND) type. Such a system undergoes
decoherence without dissipation of energy. The master equation for the evolution of
such a system under the influence of a squeezed thermal bath is obtained. From the
master equation it can be seen explicitly that the process involves decoherence without
any dissipation. The decoherence causing term in the high and zero temperature limits
are obtained and are seen to match with known results in the different temperature
regimes for the case of a thermal bath. A comparison is made between the quantum
statistical properties of QND and non-QND (i.e., involving decoherence as well as
dissipation) types of evolution (ref. [9]).
• The equation for the Wigner function describing the reduced dynamics of a single har-
monic oscillator, coupled to an oscillator bath, was obtained by Karrlein and Grabert
[Phys. Rev. E 55, 153 (1997)]. It was shown that for thermal initial conditions the
equation reduces, in the classical limit, to the corresponding classical Fokker-Planck
equation obtained by Adelman [J. Chem Phys. 64, 124 (1976)]. However for sep-
17
arable initial conditions the Adelman equations were not recovered. This paradox
involving the classical limit of a single harmonic oscillator, coupled to an oscillator
bath for different initial conditions of the system, both separable as well as thermal
initial conditions, is resolved in this work thereby clarifying the physical relevance of
different initial conditions. It is shown that for separable initial conditions, the classi-
cal Langevin equation obtained from the oscillator bath model is somewhat different
from the one considered by Adelman. The corresponding Fokker-Planck equation is
obtained and is shown to exactly match with the classical limit of the equation for the
Wigner function obtained from the master equation for separable initial conditions.
The reason why thermal initial conditions correspond to Adelman’s solution is also
discussed (ref. [10]).
• For a realistic, experimental realization of Quantum Information, it is essential to have
an understanding of Open Quantum Systems. Here an introduction, partly aimed at
students, is provided to some aspects of Open Quantum Systems which are of particular
relevance to Quantum Information. This is followed by some simple applications such
as Geometric Phase, Channel Capacity, Cryptography and a Deleter (ref. [1]).
2 Mathematical Physics
• The general problem of a single two-level atom interacting with a multimode radiation
field (without the rotating-wave approximation) which is additionally coupled to a
thermal reservoir is considered. Using the method of bosonization of the spin operators
in the Hamiltonian, and working in the Bargmann representation for all the boson
operators, the propagator for the composite system is obtained using the techniques
of functional integration, under a reasonable approximation scheme. The propagator
is explicitly evaluated for a simplified version of the system with one spin and coupled
single-mode field. The results are checked on a model describing damped harmonic
oscillator (ref. [2]).
18
• Canonical transformations on Fock space are studied using the coherent (normalized
exponential) and the ultracoherent vectors. The connection between the Weyl oper-
ator and homogeneous canonical transformations is presented and its action on the
coherent and the ultracoherent vector is given. The group action of the unitary ray
representations of the canonical group, in Fock space, is illustrated by its action on
the exponential and the ultracoherent vectors. The action of a generalized quadratic
Hamiltanian, using its differential operator form in the Bargmann-Fock Space, on the
ultracoherent functions is studied (ref. [5]).
• In the scheme of a quantum non-demolition (QND) measurement, an observable is
measured without perturbing its evolution. QND measurement schemes have been
suggested to be able to surpass the standard quantum limit of phase measurements
and reach the Heisenberg limit. In this work such shemes are studied taking the ef-
fect of decoherence into consideration. A study is made of a number of QND ‘Open
System’ Hamiltonians and their propagators are obtained. Two of these propagators
are shown to be connected to the squeezing and rotation operations. Squeezing and
rotation being both phase space area-preserving canonical transformations, this brings
out an interesting connection between the energy-preserving QND Hamiltonians and
homogeneous linear canonical transformations. Using the methods of functional in-
tegration and bosonization the details of these QND propagators and some of their
variants are worked out. The explicit determination of the propagators of these many-
body systems could apart from their technical relevance also shed some light on the
problem of QND measurement schemes (refs. [8,7]).
• In this work a graphical representation of quantum states is proposed. Pure states
require weighted digraphs with complex weights, while mixed states need, in general,
edge weighted digraphs with loops; constructions which, to the best of our knowl-
edge, are new in the theory of graphs. Both the combinatorial as well as the signless
19
Laplacian are used for graph representation of quantum states. We also provide some
interesting analogies between physical processes and graph representations. Entangle-
ment between two qubits is approached by the development of graph operations that
simulate quantum operations, resulting in the generation of Bell and Werner states. As
a biproduct, the study also leads to separability criteria using graph operations. This
paves the way for a study of genuine multipartite correlations using graph operations
(ref. [39]).
• We implement a graph theoretical realization of local unitary transformations, imple-
mented by single qubit Pauli gates, by adapting techniques of graph switching. This
leads to the concept of local unitary equivalent graphs. We illustrate our method by a
few, well known, local unitary transformations implemented by single qubit Pauli and
Hadamard gates. The work is then extended to provide a graphi- cal implementation
of CNOT gates. The well known two-qubit entangled states, Bell states, are shown
to emerge from our constructions. We thus have a graphical realization of universal
quantum computation (ref. [49]).
• We consider the separability problem for bipartite quantum states arising from graphs.
Earlier it was proved that the degree criterion is the graph theoretical counterpart of
the familiar PPT criterion for separability, although there are entangled states with
positive partial transpose for which degree criterion fails. Here, we introduce the
concept of partially symmetric graphs and degree symmetric graphs by using the well-
known concept of partial transposition of a graph and degree criteria, respectively.
Thus, we provide classes of bipartite separable states of dimension m× n arising from
partially symmetric graphs. We identify partially asymmetric graphs which lack the
property of partial symmetry. Finally we develop a combinatorial procedure to create
a partially asymmetric graph from a given partially symmetric graph. We show that
this combinatorial operation can act as an entanglement generator for mixed states
20
arising from partially symmetric graphs (ref. [63]).
• Construction of graphs with equal eigenvalues (co-spectral graphs) is an interesting
problem in spectral graph theory. Seidel switching is a well-known method for gener-
ating co-spectral graphs. From a matrix theoretic point of view, Seidel switching is a
combined action of a number of unitary operations on graphs. Recently, it has been
shown that significant connections between graph and quantum information theories.
Corresponding to Laplacian matrices of any graph there are quantum states useful in
quantum computing. From this point of view, graph theoretical problems are mean-
ingful in the context of quantum information. This work describes Seidel switching
from a quantum perspective. Here, we generalize Seidel switching to weighted directed
graphs. We use it to construct graphs with equal Laplacian and signless Laplacian
spectra and consider density matrices corresponding to them. Hence Seidel switching
is a technique to generate cospectral density matrices. Next, we show that all the uni-
tary operators used in Seidel switching are global unitary operators. Global unitary
operators can be used to generate entanglement, a benchmark phenomena in quantum
information processing (ref. [67]).
• Quantum discord refers to an important aspect of quantum correlations for bipartite
quantum systems. In our earlier works we have shown that corresponding to every
graph (combinatorial) there are quantum states whose properties are reflected in the
structure of the corresponding graph. Here, we attempt to develop a graph theoretic
study of quantum discord that corresponds to a necessary and sufficient condition of
zero quantum discord states which says that the blocks of density matrix correspond-
ing to a zero quantum discord state are normal and commute with each other. These
blocks have a one to one correspondence with some specific subgraphs of the graph
which represents the quantum state. We obtain a number of graph theoretic properties
representing normality and commutativity of a set of matrices which are indeed arising
21
from the given graph. Utilizing these properties we define graph theoretic measures
for normality and commutativity that results a formulation of graph theoretic quan-
tum discord. We identify classes of quantum states with zero discord using the said
formulation (ref. [68]).
• In this paper we determine the class of quantum states whose density matrix representa-
tion can be derived from graph Laplacian matrices associated with a weighted directed
graph and we call them graph Laplacian quantum states. Then we obtain structural
properties of these graphs such that the corresponding graph Laplacian states have
zero quantum discord by investigating structural properties of clustered graphs which
provide a family of commuting normal matrices formed by the blocks of its Laplacian
matrices. We apply these results on some important mixed quantum states, such as
the Werner, Isotropic, and X-states (ref. [69]).
3 Dynamics of entanglement and Quantum Correla-
tions in open quantum systems
• We analyze the dynamics of entanglement in a two-qubit system interacting with an
initially squeezed thermal environment via a quantum nondemolition system-reservoir
interaction, with the system and reservoir assumed to be initially separable. We com-
pare and contrast the decoherence of the two-qubit system in the case where the qubits
are mutually close-by (‘collective regime’) or distant (‘localized regime’) with respect to
the spatial variation of the environment. Sudden death of entanglement (as measured
by concurrence) is shown to occur in the localized case rather than in the collective
case, where entanglement tends to ‘ring down’. Using a novel quantification of mixed
state entanglement, we show that there are noise regimes where even though entangle-
ment (as measured by concurrence) vanishes, the state is still available for applications
like NMR quantum computation, because of the presence of a pseudo-pure component.
The dynamics is found to satisfy a spin-flip symmetry operation. We give an effective
22
temperature dependent dynamics for the collective decoherence regime and make an
application of the two-qubit dynamics to quantum communication, by using it on a
simplified model of quantum repeaters (ref. [21]).
• We study the dynamics of entanglement in a two-qubit system interacting with a
squeezed thermal bath via a dissipative system-reservoir interaction with the system
and reservoir assumed to be in a separable initial state. The resulting entanglement is
studied by making use of a recently introduced measure of mixed state entanglement
via a probability density function which gives a statistical and geometrical characteri-
zation of entanglement by exploring the entanglement content in the various subspaces
spanning the two-qubit Hilbert space. We also make an application of the two-qubit
dissipative dynamics to a simplified model of quantum repeaters (ref. [22]).
• The effect of a number of mechanisms designed to suppress decoherence in open quan-
tum systems are studied with respect to their effectiveness at slowing down the loss
of entanglement. The effect of photonic band-gap materials and frequency modulation
of the system-bath coupling are along expected lines in this regard. However, other
control schemes, like resonance fluorescence, achieve quite the contrary: increasing
the strength of the control kills entanglement off faster. The effect of dynamic de-
coupling schemes on two qualitatively different system-bath interactions are studied
in depth. Dynamic decoupling control has the expected effect of slowing down the
decay of entanglement in a two-qubit system coupled to a harmonic oscillator bath
under non-demolition interaction. However, non-trivial phenomena are observed when
a Josephson charge qubit, strongly coupled to a random telegraph noise bath, is sub-
ject to decoupling pulses. The most striking of these reflects the resonance fluorescence
scenario in that an increase in the pulse strength decreases decoherence but also speeds
up the sudden death of entanglement. This demonstrates that the behaviour of deco-
herence and entanglement in time can be qualitatively different in the stong-coupling
23
non-Markovian regime (ref.[31]).
• In this work, we study quantum correlations in mixed states. The states studied
are modeled by a two-qubit system interacting with its environment via a quantum
non demolition (purely dephasing) as well as dissipative type of interaction. The
entanglement dynamics of this two qubit system is analyzed. We make a comparative
study of various measures of quantum correlations, like Concurrence, Bell’s inequality,
Discord and Teleportation fidelity, on these states, generated by the above evolutions.
We classify these evoluted states on basis of various dynamical parameters like bath
squeezing parameter r, inter-qubit spacing r12, temperature T and time of system-
bath evolution t. In this study, in addition we report the existence of entangled states
which do not violate Bell’s inequality, but can still be useful as a potential resource
for teleportation. Moreover we study the dynamics of quantum as well as classical
correlation in presence of dissipative coherence (ref.[26]).
• The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle
can be demonstrated in various ways that do not necessarily provide a geometry-
independent description. For example, the position probability distribution becomes
increasingly Gaussian, with a concomitant fall in the standard deviation, in the former
case, but not in the latter. As another example, each step of the quantum walk on a
line may be subjected to an arbitrary phase gate, without affecting the position prob-
ability distribution, no matter whether the walk is noiseless or noisy. This symmetry,
which is absent in the case of noiseless cyclic walk, but is restored in the presence of
sufficient noise, serves as an indicator of classicalization, but only in the cyclic case.
Here we show that the degree of quantum correlations between the coin and position
degrees of freedom, quantified by a measure based on the disturbance induced by local
measurements [Luo, Phys. Rev. A 77, 022301 (2008)], provides a suitable measure of
classicalization across both type of walks. Applying this measure to compare the two
24
walks, we find that cyclic quantum walks tend to classicalize faster than quantum walks
on a line because of more efficient phase randomization due to the self-interference of
the two counter-rotating waves. We model noise as acting on the coin, and given by
the squeezed generalized amplitude damping (SGAD) channel, which generalizes the
generalized amplitude damping channel (ref.[27]).
• We present a novel scheme for generating entanglement between two spatially sepa-
rated systems. The scheme makes use of the spatial entanglement generated by the
interference effect during the evolution of a single-particle quantum walk. Any two
systems which can interact with the spatial modes entangled during the walk evolu-
tion can be entangled using this scheme. A notable feature is the ability to control the
quantum walk dynamics and its localization in position space resulting in a substan-
tial control and improvement in the entanglement output. Different implementation
schemes to entangle spatially separated atoms using quantum walk on a photon or a
single atom are presented (ref.[28]).
• Noisy quantum walks are studied from the perspective of comparing their quantumness
as defined by two popular measures, measurement-induced disturbance (MID) and
quantum discord (QD). While the former has an operational definition, unlike the
latter, it also tends to overestimate non-classicality because of lack of optimization over
local measurements. Applied to quantum walks, we find that MID, while acting as a
loose upper bound on QD, still tends to reflect well trends in the behavior of the latter.
However, there are regimes where its behavior is not indicative of non-classicality: in
particular, we find an instance where MID increases with the application of noise,
where we expect a reduction of quantumness (ref.[30]).
• Quantum discord is a prominent measure of quantum correlations, playing an impor-
tant role in expanding its horizon beyond entanglement. Here we provide an oper-
ational meaning of (geometric) discord, which quantifies the amount of non-classical
25
correlation of an arbitrary quantum system based on its minimal distance from the set
of classical states, in terms of teleportation fidelity for general two qubit and d⊗ d di-
mensional isotropic and Werner states. A critical value of the discord is found beyond
which the two qubit state must violate the Bell inequality. This is illustrated by an
open system model of a dissipative two qubit. For the d ⊗ d dimensional states the
lower bound of discord is shown to be obtainable from an experimentally measurable
witness operator (ref. [41]).
• Bipartite entangled states in arbitrary dimensions are studied and different bounds for
the teleportation fidelity are obtained. In addition, various relations between telepor-
tation fidelity and the entanglement measures depending upon Schmidt rank of the
states are established. These relations and bounds help in to determine the amount
of entanglement required for teleportation. This amount of entanglement required for
teleportation is called “Entanglement of Teleportation”. These bounds are used to de-
termine the teleportation fidelity as well as the entanglement required for teleportation
of states modeled by a two qutrit mixed system as well as two qubit open quantum
systems (ref. [42]).
• A master equation is constructed for a global system-bath interaction both in the
absence as well as presence of non-Markovian noise. The master equation is exactly
solved for a special class of two qubitX states (which contains Bell diagonal and Werner
states). The l1 norm of coherence is calculated and the dynamics of quantum coherence
in the presence of a global system-bath interaction is observed. It is shown that the
global part of the system-bath interaction compensates for the decoherence, resulting
in the slow down of coherence decay. The concurrence and the Fisher information,
explicitly calculated for a particular two qubit Werner state, indicate that the decay of
these quantum features also slow down under a global system-bath interaction. Also
shown is the feature that the coherence is the most robust of all the three non-classical
26
features under environmental interaction. Entanglement is seen to be the most costly
of them all. For an appropriately defined limiting case, all the three quantities show
freezing behaviour. This limiting condition is attainable when the separations between
the energy levels of both the atomic qubits are small (ref. [62]).
4 Phase distributions in open quantum systems
• The dynamics of quantum phase distribution associated with the reduced density ma-
trix of a system, as the system evolves under the influence of its environment with
a quantum nondemolition type of coupling is quantitatively analyzed. The system
is taken to be either an oscillator (harmonic or anharmonic) or a two-level atom (or
equivalently, a spin-1/2 system), and the environment modelled as a bath of harmonic
oscillators, initially in a general squeezed thermal state. The impact of the different en-
vironmental parameters is explicitly brought out on the dynamics of the quantum phase
distribution of the system starting at various initial states. The results are applicable
to a variety of physical systems now studied experimentally with QND measurements
(ref. [11]).
• The previous work is extended to study the phase distribution in QND as well as
dissipative systems. The impact of the different environmental parameters on the
dynamics of the quantum phase distribution for the system starting out in various
initial states, is explicitly brought out. An interesting feature that emerges from the
work is that the relationship between squeezing and temperature effects depends on
the type of system-bath interaction. In the case of quantum nondemolition type of
interaction, squeezing and temperature work in tandem, producing a diffusive effect on
the phase distribution. In contrast, in case of a dissipative interaction, the influence
of temperature can be counteracted by squeezing, which manifests as a resistence to
randomization of phase. The phase distributions are used to bring out a notion of
complementarity in atomic systems. A study is made of the dispersion of the phase
27
using the phase distributions conditioned on particular initial states of the system.
This would be of direct relevance to a number of experiments (ref. [14]).
5 Open quantum systems and quantum computation
• Geometric phase is intrinsically related to the kinematics of the path followed by the
system in its Hilbert space. Both from the point of view theoretical interest as well
as practical implications, as for example with respect to quantum computers, it is
interesting to study geometric phase in the context of open quantum systems. In
this work we make such a study for a number of open system models with the bath
(reservoir) being modelled as a squeezed thermal bath, with the system-bath interaction
being taken to be both non-dissipative (QND) as well as dissipative. An interesting
feature coming out of this work is the contrasting interplay between squeezing and
thermal effects in the two types of system-bath interactions. Whereas for the QND
case, squeezing plays a role similar to temperature in suppressing the geometric phase,
in the dissipative case squeezing is seen to oppose thermal effects in some regimes.
This could have practical implications in the design of realistic geometric phase gates
for quantum computation (ref. [12]).
• The work done on the reduced dynamics of the multi-qubit system in (ref. [21], [22]) is
used to compute the geometric phase of a two-qubit system interacting with its bath
via both QND as well as dissipative interactions (ref. [23]).
• Environment-induced decoherence presents a great challenge to realizing a quantum
computer. In this work is brought out the somewhat surprising fact that decoherence
can be useful, indeed necessary, for practical quantum computation, in particular, for
effective erasure of quantum memory by way of preparing the initial state of the quan-
tum computer. The environment must in general be dissipative. A specific example
is the amplitude damping channel provided by a two-level system interacting with its
28
environment in the weak Born-Markov rotating wave approximation (ref. [13]).
• Geometric phase plays an important role in evolution of pure or mixed quantum states.
However, when a system undergoes decoherence the development of geometric phase
may be inhibited. Here, we show that when a quantum system interacts with two
competing environments there can be enhancement of geometric phase. This effect
is akin to Parrondo like effect on the geometric phase which results from quantum
frustration of decoherence. Our result suggests that the mechanism of two competing
decoherence can be useful in fault tolerant holonomic quantum computation (ref. [43]).
6 Quantum communication
• A new noisy quantum channel called “The squeezed generalized amplitude damping
channel” is introduced, which depicts the physics of dissipative interaction with a
squeezed thermal bath, governed by a Lindblad-type evolution. The action of this
channel is given in terms of Kraus operators. As expected, this channel reduces to the
“generalized amplitude damping channel” when the squeezing parameters are set to
zero. This work brings out the physics behind this new channel, its implications and
properties. As an application of this channel to quantum communication, its classical
capacity is studied (ref. [20]).
• The principle of a cryptographic switch is illustrated using a quantum system, in which
a third party (Charlie) can control to a continuously varying degree the amount of in-
formation the receiver (Bob) receives, after the sender (Alice) has sent her information.
Suppose Charlie transmits a Bell state to Alice and Bob. Alice uses dense coding to
transmit two bits to Bob. Only if the 2-bit information corresponding to choice of Bell
state is made available by Charlie to Bob can the latter recover Alice’s information.
By varying the information he gives, Charlie can continuously vary the information
recovered by Bob. The performance of the protocol subjected to the squeezed general-
29
ized amplitude damping channel is considered. A number of practical situations where
a cryptographic switch would be of use are presented (ref. [35]).
• We shown that a realistic, controlled bidirectional remote state preparation is possible
using a large class of entangled quantum states having a particular structure. Existing
protocols of probabilistic, deterministic and joint remote state preparation are gener-
alized to obtain the corresponding protocols of controlled bidirectional remote state
preparation (CBRSP). A general way of incorporating the effects of two well known
noise processes, the amplitude-damping and phase-damping noise, on the probabilistic
CBRSP process is studied in detail by considering that noise only affects the travel
qubits of the quantum channel used for the probabilistic CBRSP process. Also indi-
cated is how to account for the effect of these noise channels on deterministic and joint
remote state CBRSP protocols (ref. [50]).
• The effect of noise on various protocols of secure quantum communication has been
studied. Specifically, we have investigated the effect of amplitude damping, phase
damping, squeezed generalized amplitude damping, Pauli type as well as various col-
lective noise models on the protocols of quantum key distribution, quantum key agree-
ment,quantum secure direct quantum communication and quantum dialogue. From
each type of protocol of secure quantum communication, we have chosen two protocols
for our comparative study; one based on single qubit states and the other one on entan-
gled states. The comparative study reported here has revealed that single-qubit-based
chemes are generally found to perform better in the presence of amplitude damping,
phase damping, squeezed generalized amplitude damping noises, while entanglement-
based protocols turn out to be preferable in the presence of collective noises. It is
also observed that the effect of noise entirely depends upon the number of rounds of
quantum communication involved in a scheme of quantum communication. Further,
it is observed that squeezing, a completely quantum mechanical resource present in
30
the squeezed generalized amplitude channel, can be used in a beneficial way as it may
yield higher fidelity compared to the corresponding zero squeezing case (ref. [64]).
• A set of schemes for secure quantum communication are analyzed under the influence
of non-Markovian channels. By comparing with the corresponding Markovian cases, it
is seen that the average fidelity in all these schemes can be maintained for relatively
longer periods of time. Effects of non-Markovinan noise on a number of facets of quan-
tum cryptography, such as quantum secure direct communication, deterministic secure
quantum communication and their controlled counterparts, such as quantum dialogue,
quantum key distribution, quantum key agreement have been extensively investigated.
Specifically, a scheme for controlled quantum dialogue (CQD) is analyzed over damp-
ing, dephasing and depolarizing non-Markovian channels, and subsequently, the effect
of these non-Markovian channels on the other schemes of ecure quantum communi-
cation is deduced from the results obtained for CQD. The damped non-Markovian
channel causes, a periodic revival in the fidelity; while fidelity is observed to be sus-
tained under the influence of the dephasing non-Markovian channel. The depolarizing
channel, as well as the other non-Markovian channels discussed here, show that the ob-
tained average fidelity subjected to noisy environment depend on the coupling strength
and the number of rounds of quantum communication involved in a particular scheme
(ref. [66]).
• Quantum Key Distribution (QKD) is a key exchange protocol which is implemented
over free space optical links and optical fiber cable. When direct communication is
not possible, QKD is performed over fiber cables, but the imperfections in detectors
used at receiver side and also the material properties of fiber cables limit the long
distance communication. Free space based quan- tum key distribution is free from
such limitations, and can pave way for satellite based quantum communication to set
up a global network for sharing secret messages. To implement free space optical (FSO)
31
links, it is essential to study the effect of atmospheric turbulence. Here, an analysis is
made for satellite based quantum communication using QKD protocols. The results
obtained indicate that SARG04 protocol is an effective approach for satellite based
quantum communication (ref. [77]).
• In quantum key distribution, one conservatively assumes that the eavesdropper Eve is
restricted only by physical laws, whereas the legitimate parties, namely the sender Alice
and receiver Bob, are subject to realistic constraints, such as noise due to environment-
induced decoherence. In practice, Eve too may be bound by the limits imposed by
noise, which can give rise to the possibility that decoherence works to the advantage of
the legitimate parties. A particular scenario of this type is one where Eve can’t replace
the noisy communication channel with an ideal one, but her eavesdropping channel
itself remains noiseless. Here, we point out such a situation, where the security of the
Ping-Pong protocol (modified to a key distribution scheme) against a noise-restricted
adversary improves under a non-unital noisy channel, but deteriorates under unital
channels (ref. [78]).
7 Quantum information
• A study is made of some discrete symmetries of unbiased (Hadamard) and biased
quantum walks on a line, which are shown to hold even when the quantum walker is
subjected to environmental effects. The noise models considered in order to account
for these effects are the phase flip, bit flip and generalized amplitude damping chan-
nels. The numerical solutions are obtained by evolving the density matrix, but the
persistence of the symmetries in the presence of noise is proved using the quantum
trajectories approach. These investigations can be relevant to the implementation of
quantum walks in various known physical systems. Implementation of these ideas in
the case of NMR quantum information processor and ultra cold atoms is discussed (ref.
[18]).
32
• Augmenting the unitary transformation which generates a quantum walk by a general-
ized phase gate G is a symmetry for both noisy and noiseless quantum walk on a line,
in the sense that it leaves the position probability distribution invariant. However,
this symmetry breaks down in the case of a quantum walk on an n-cycle, and hence
can be regarded as a probe of the walk topology. Noise, modelled here as phase flip
and generalized amplitude damping channels, tends to restore the symmetry because
it classicalizes the walk. However, symmetry restoration happens even in the regime
where the walker is not entirely classical, because noise also has the effect of desensi-
tizing the operation G to the walk topology. This provides a nontrivial instance of the
interplay between geometry and noise in a quantum information processing system. We
discuss methods for physical implementation, and talk about the wider implications to
condensed matter systems (ref. [19]).
• Quantum walk models have been used as an algorithmic tool for quantum computation
and to describe various physical processes. This paper revisits the relationship between
relativistic quantum mechanics and the quantum walks. We show the similarities of
the mathematical structure of the decoupled and coupled form of the discrete-time
quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the
latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-
time quantum walk as a coupled form of the continuous-time quantum walk is also
shown by transforming the decoupled form of the discrete-time quantum walk to the
Schrodinger form. By showing the coin to be a means to make the walk reversible, and
that the Dirac-like structure is a consequence of the coin use, our work suggests that
the relativistic causal structure is a consequence of conservation of information. How-
ever, decoherence (modelled by projective measurements on position space) generates
entropy that increases with time, making the walk irreversible and thereby producing
an arrow of time. Lieb-Robinson bound is used to highlight the causal structure of the
quantum walk to put in perspective the relativistic structure of quantum walk, maxi-
33
mum speed of the walk propagation and the earlier findings related to the finite spread
of the walk probability distribution. We also present a two-dimensional quantum walk
model on a two state system to which the study can be extended (ref.[24]).
• Single-qubit channels are studied under two broad classes: amplitude damping channels
and generalized depolarizing channels. A canonical derivation of the Kraus represen-
tation of the former, via the Choi isomorphism is presented for the general case of a
system’s interaction with a squeezed thermal bath. This isomorphism is also used to
characterize the difference in the geometry and rank of these channel classes. Under
the isomorphism, the degree of decoherence is quantified according to the mixedness
or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the
former channels do not form a convex set as seen from an ab initio perspective. Fur-
ther, where the rank of generalized depolarizing channels can be any positive integer
upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance
parameters are used to bring out the different influences of temperature and squeezing
in dissipative channels. In particular, a noise range is identified where the distin-
guishability of states improves inspite of increasing decoherence due to environmental
squeezing. (ref. [40])
• On account of the Abel-Galois no-go theorem for the algebraic solution to quintic and
higher order polynomials, the eigenvalue problem and the associated characteristic
equation for a general noise dynamics in dimension d via the Choi-Jamiolkowski ap-
proach cannot be solved in general via radicals. A way around this impasse is provided
by decomposing the Choi matrix into simpler, not necessarily positive, Hermitian oper-
ators that are diagonalizable via radicals, which yield a set of ‘positive’ and ‘negative’
Kraus operators. The price to pay is that the sufficient number of Kraus operators is d4
instead of d2, sufficient in the Kraus representation. We consider various applications
of the formalism: the Kraus repesentation of the 2-qubit amplitude damping channel,
34
the noise resulting from a 2-qubit system interacting dissipatively with a vacuum bath;
defining the maximally dephasing and purely dephasing components of the channel
in the new representation, and studying their entanglement breaking and broadcast
properties (ref. [44]).
• Quantum Algorithms have long captured the imagination of computer scientists and
physicists primarily because of the speed up achieved by them over their classical
counterparts using principles of quantum mechanics. Entanglement is believed to be
the primary phenomena behind this speed up. However their precise role in quantum
algorithms is yet unclear. In this article, we explore the nature of entanglement in
the Grovers search algorithm. This algorithm enables searching of elements from an
unstructured database quadratically faster than the best known classical algorithm.
Geometric measure of entanglement has been used to quantify and analyse entangle-
ment across iterations of the algorithm. We reveal how the entanglement varies with
increase in the number of qubits and also with the number of marked or solution states.
Numerically, it is seen that the behaviour of the maximum value of entanglement is
monotonous with the number of qubits. Also, for a given value of the number of
qubits, a change in the marked states alters the amount of entanglement. The amount
of entanglement in the final state of the algorithm has been shown to depend solely
on the nature of the marked states. Explicit analytical expressions are given showing
the variation of entanglement with the number of iterations and the global maximum
value of entanglement attained across all iterations of the algorithm (ref. [46]).
8 Error Correction
• Characterizing noisy quantum processes is important to quantum computation and
communication (QCC), since quantum systems are generally open. To date, all meth-
ods of characterization of quantum dynamics (CQD), typically implemented by quan-
tum process tomography, are off-line, i.e., QCC and CQD are not concurrent, as they
35
require distinct state preparations. Here we introduce a method, quantum error cor-
rection based characterization of dynamics (QECCD), in which the initial state is any
element from the code space of a quantum error correcting code that can protect the
state from arbitrary errors acting on the subsystem subjected to the unknown dynam-
ics. The statistics of stabilizer measurements, with possible unitary pre-processing
operations, are used to characterize the noise, while the observed syndrome can be
used to correct the noisy state. Our method requires at most 2(4n1) configurations to
characterize arbitrary noise acting on n qubits (ref. [48]).
• A quantum error correcting code is a subspace C such that allowed errors acting on
any state in C can be corrected. A quantum code for which state recovery is only
required up to a logical rotation within C, can be used for detection of errors, but not
for quantum error correction. Such a code with stabilizer structure, which we call an
ambiguous stabilizer code (ASC), can nevertheless be useful for the characterization
of quantum dynamics (CQD). The use of ASCs can help lower the size of CQD probe
states used, but at the cost of increased number of operations (ref. [47]).
• The method of quantum error correction based characterization of quantum dynamics
(QECCD) is applied to developing a protocol for performing quantum process tomog-
raphy on a two-qubit system interacting dissipatively with a vacuum bath. The method
uses a 5-qubit quan- tum error correcting code that corrects arbitrary errors on the
first two qubits, and thus saturates the quantum Hamming bound. The noise model
considered allows for both correlated and independent noise on the two-qubit system.
Identifying the degree of correlation of the noise with the departure of the correspond-
ing process matrix from the product form, we study its dependence on the time of
evolution and inter-qubit separation. We find that the noise correlation (maximized
over time) falls monotonically with inter-qubit separation. Time evolution of the noise
correlation shows different behavior for collective vs independent noise: in both cases,
36
it attains a limiting value, but shows initial oscillatory behavior in the former case (ref.
[61]).
9 Open quantum sytems & Foundations of quantum
mechanics
• Quantum theory of Stern-Gerlach System in contact with a lineraly dissipative environ-
ment at an arbitrary temperature is studied. Here use is made of the Feynman-Vernon
influence functional technique generalized to incorporate non-separable initial condi-
tions. The behaviour of the density matrix in the long-time limit is analyzed and the
time scale of decay of the elements off-diagonal in the coordinate and momentum space
are computed for the entire temperature range (ref. [1]).
• An information theoretic interpretation of the number-phase complementarity in atomic
systems is developed, where phase is treated as a continuous positive operator valued
measure (POVM). The relevant uncertainty principle is obtained as an upper bound
on a sum of knowledge of these two observables for the case of two-level systems. A
tighter bound characterizing the uncertainty relation is obtained numerically in terms
of a weighted knowledge sum involving these variables. We point out that complemen-
tarity in these systems departs from mutual unbiasededness in two signalificant ways:
first, the maximum knowledge of a POVM variable is less than log(dimension) bits;
second, surprisingly, for higher dimensional systems, the unbiasedness may not be mu-
tual but unidirectional in that phase remains unbiased with respect to number states,
but not vice versa. Finally, we study the effect of non-dissipative and dissipative noise
on these complementary variables for a single-qubit system (ref. [15]).
• A unified, information theoretic interpretation of the number-phase complementarity
that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscil-
lator) systems is developed, with number treated as a discrete Hermitian observable
37
and phase as a continuous positive operator valued measure (POVM). The relevant
uncertainty principle is obtained as a lower bound on entropy excess, X, the difference
between the entropy of one variable, typically the number, and the knowledge of its
complementary variable, typically the phase, where knowledge of a variable is defined
as its relative entropy with respect to the uniform distribution. In the case of finite
dimensional systems, a weighting of phase knowledge by a factor µ (> 1) is necessary
in order to make the bound tight, essentially on account of the POVM nature of phase
as defined here. Numerical and analytical evidence suggests that µ tends to 1 as sys-
tem dimension becomes infinite. We study the effect of non-dissipative and dissipative
noise on these complementary variables for oscillator as well as atomic systems (ref.
[16], [17]).
10 Non-Markovian Physics
• In the case of the discrete time coined quantum walk the reduced dynamics of the
coin shows non-Markovian recurrence features due to information back-flow from the
position degree of freedom. Here we study how this non-Markovian behavior is modified
in the presence of open system dynamics. In the process, we obtain useful insights into
the nature of non-Markovian physics. In particular, we show that in the case of (non-
Markovian) random telegraph noise (RTN), a further discernible recurrence feature is
present in the dynamics. Moreover, this feature is correlated with the localization of
the walker. On the other hand, no additional recurruence feature appears for other
non-Markovian types of noise (Ornstein-Uhlenbeck and Power Law noise). We propose
a power spectral method for comparing the relative strengths of the non-Markovian
component due to the external noise and that due to the internal position degree of
freedom (ref. [73]).
• Quantum non-Markovianity of a quantum noisy channel manifests typically as informa-
tion backflow, characterized by the departure of the intermediate map from complete
38
positivity, though we indicate certain noisy channels that don’t exhibit this behavior.
In complex systems, non-Markovianity becomes more involved on account of subsystem
dynamics. Here we study various facets of non-Markovian evolution, in the context of
coined quantum walks, with particular stress on disambiguating the internal vs. envi-
ronmental contributions to non-Markovian backflow. For the above problem of disam-
biguation, we present a general power-spectral technique based on a distinguishability
measure such as trace-distance or correlation measure such as mutual information. We
also study various facets of quantum correlations in the transition from quantum to
classical random walks, under the considered non-Markovian noise models. The poten-
tial for the application of this analysis to the quantum statistical dynamics of complex
systems is indicated (ref. [74]).
• Non-Markovian quantum effects are typically observed in systems interacting with
structured reservoirs. Discrete-time quantum walks are prime example of such sys-
tems in which, quantum memory arises due to the controlled interaction between the
coin and position degrees of freedom. Here we show that the information backflow
that quantifies memory effects can be enhanced when the particle is subjected to un-
correlated static or dynamic disorder. The presence of disorder in the system leads
to localization effects in 1-dimensional quantum walks. We shown that it is possible
to infer about the nature of localization in position space by monitoring the infor-
mation backflow in the reduced system. Further, we study other useful properties of
the reduced system such as entanglement, interference and its connection to quantum
non-Markovianity (ref. [76]).
• We introduce a method to construct non-Markovian variants of completely positive
(CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity
with the breakdown in CP-divisibility of the map, i.e., appearance of a not-completely-
positive (NCP) intermediate map. In particular, we consider the case of non-Markovian
39
dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map
crossover at a point which corresponds to a singularity in the canonical decoherence
rate of the corresponding master equation, and thus to a momentary non-invertibility
of the map. Thereater, the rate becomes negative, indicating non-Markovianity. We
quantify the non-Markovianity by two methods, one based on CP-divisibility (Hall et
al., PRA 89, 042120, 2014), which doesn’t require optimization but requires normaliza-
tion to handle the singularity, and another method, based on distinguishability (Breuer
et al. PRL 103, 210401, 2009), which requires optimization but is insensitive to the
singularity (ref. [80]).
• We study the violations of Leggett-Garg (LG) inequality in a qubit subjected to
non-Markovian noisy channels such as Random Telegraph Noise (RTN) and Ornstein-
Uhlenbeck Noise (OUN). Quite generally, the state-independence of the violation in
the noiseless case is preserved under the application of noise. Within a given family of
noisy channels (in specific, RTN or OUN), we find an enhancement in the violation in
the non-Markovian case as compared to the Markovian case. We thus find that non-
Markovianity provides a stronger demonstration of quantumness of the system (ref.
[81]).
11 Quantum Thermodynamics
• We show that non-Markovian effects of the reservoirs can be used as a resource to
extract work from an Otto cycle. The state transformation under non-Markovian dy-
namics is cast into a two-step process involving an isothermal process using a Marko-
vian reservoir followed by an adiabatic process. From second law of thermodynamics,
we show that the maximum amount of extractable work from the state prepared un-
der the non-Markovian dynamics quantifies the lower bound of non-Markovianity. We
illustrate our ideas with an explicit example of non-Markovian evolution (ref. [75]).
40
12 Relativistic Quantum Information
• We make use of the tools of quantum information theory to shed light on the Unruh
effect. Here we study various facets of quantum correlations, such as, Bell inequality
violations, entanglement, teleportation and measurement induced decoherence under
the effect of the Unruh channel. The Unruh channel for a mode of a free Dirac field,
as seen by a relativistically accelerated observer, is seen to be noisy and is character-
ized, in this work, by providing its operator-sum representation. A modal qubit thus
appears as if subjected to quantum noise that degrades quantum information, as ob-
served in the accelerated reference frame. We compare and contrast this noise, which
arises from the Unruh effect, from a conventional noise due to environmental decoher-
ence. We show that the Unruh effect produces an amplitude-damping-like channel,
associated with zero temperature, even though the Unruh effect is associated with a
non-zero temperature. Asymptotically, the Bloch sphere subjected to the channel does
not converge to a point, as would be expected by fluctuation-dissipation arguments,
but contracts by a finite factor. We construct for the Unruh effect the inverse chan-
nel, a non-completely-positive map, that reverses the effect, and offer some physical
interpretation (ref. [53]).
• A Bloch vector representation of Unruh channel for a Dirac field mode is developed.
This is used to provide a unified, analytical treatment of quantum Fisher and Skew
information for a qubit subjected to the Unruh channel, both in its pure form as well
as in the presence of experimentally relevant external noise channels. The time evo-
lution of Fisher and Skew information is studied along with the impact of external
environment parameters such as temperature and squeezing. The external noises are
modelled by both purely dephasing phase damping as well as the squeezed generalized
amplitude damping channels. An interesting interplay between the external reservoir
temperature and squeezing on the Fisher and Skew information is observed, in par-
41
ticular, for the action of the squeezed generalized amplitude damping channel. It is
seen that for some regimes, squeezing can enhance the quantum information against
the deteriorating influence of the ambient environment. Similar features are also ob-
served for the analogous study of Skew information, highlighting the similar origin of
the Fisher and Skew information (ref. [60]).
• We show through the Choi matrix approach that the effect of Unruh acceleration on
a qubit is similar to the interaction of the qubit with a vacuum bath, despite the
finiteness of the Unruh temperature. Thus, rather counterintuitvely, from the perspec-
tive of decoherence in this framework, the particle experiences a vacuum bath with a
temperature-modified interaction strength, rather than a thermal bath. We investigate
how this ”relativistic decoherence” is modified by the presence of environmentally in-
duced decoherence, by studying the degradation of quantum information, as quantified
by parameters such as nonlocality, teleportation fidelity, entanglement, coherence and
quantum measurement-induced disturbance (a discord-like measure). Also studied are
the performance parameters such as gate and channel fidelity. We highlight the dis-
tinction between dephasing and dissipative environmental interactions, by considering
the actions of quantum non-demolition and squeezed generalized amplitude damping
channels, respectively, where, in particular, squeezing is shown to be a useful quantum
resource (ref. [65]).
13 Particle Physics and Foundations of Quantum Me-
chanics
• We study the impact of decoherence on B meson systems with specific emphasis on Bs
. For consistency we also study the Bd mesons based on the most recent data. We find
that the Bd mesons are 34 away from total decoherence, while the Bs mesons are seen
to be upto 31 away from total decoherence. Thus, our results prove, with experimental
verity, that neutral meson systems are free from decoherence effects. Therefore, this
42
provides a very useful laboratory for testing the foundations of quantum mechanics
(ref. [45]).
• The interplay between the various measures of quantum correlations are well known
in stable optical and electronic systems. Here we study such foundational issues in
unstable quantum systems. Specifically we study meson-antimeson systems (KK,
BdBd and BsBs), which are produced copiously in meson factories. In particular,
the nonclassicality of quantum correlations which can be characterized in terms of
nonlocality (which is the strongest condition), entanglement, teleportation fidelity or
weaker nonclassicality measures like quantum discord are analyzed. We also study the
impact of decoherence on these measures of quantum correlations, using the semigroup
formalism. A comparison of these measures brings out the fact that the relations
between them can be nontrivially different from those of their stable counterparts such
as neutrinos (ref. [54]).
• Neutrino oscillations provide evidence for the mode entanglement of neutrino mass
eigenstates in a given flavour eigenstate. Given this mode entanglement, it is pertinent
to ask if other quantum correlations are present in neutrino evolution. In this study,
we compute a number of such correlations in the approximation of two flavour neutrino
oscillations. We find that Bell’s inequality is always violated. The various facets of
quantum correlations are very closely tied to the neutrino mixing angle. The point of
minimum survival probability corresponds to the extremum point of all measures of
quantum correlations. This extremum is a maximum for mixing angles below a critical
value and a minimum for above the critical value (ref. [55]).
• Correlations exhibited by neutrino oscillations are studied via quantum information
theoretic quantities. We show that the strongest type of entanglement, genuine mul-
tipartite entanglement, is persistent in the flavour changing states. We prove the exis-
tence of Bell type nonlocal features, in both its absolute and genuine tripartite avatars.
43
Finally, we show that a measure of nonclassicality, dissension, which is a generalization
of quantum discord to the tripartite case, is nonzero for almost the entire range of
time in the evolution of an initial electron-neutrino. Via these quantum information
theoretic quantities capturing different aspects of quantum correlations, we elucidate
the differences between the flavour types, shedding light on the quantum-information
theoretic aspects of the weak force (ref. [56]).
• In the time evolution of neutral meson systems, a perfect quantum coherence is usually
assumed. The important quantities of the B0d system, such as sin 2β and ∆md, are
determined under this assumption. However, the meson system interacts with its
environment. This interaction can lead to decoherence in the mesons even before they
decay. In our formalism this decoherence is modelled by a single parameter λ. It is
desirable to re-examine the procedures of determination of sin 2β and ∆md in meson
systems with decoherence. We find that the present values of these two quantities are
modulated by λ. Re-analysis of B0d data from B-factories and LHCb can lead to a
clean determination of λ, sin 2β and ∆md (ref. [57, 2]).
• We study the geometric phase for neutrinos at various man-made facilities, such as
the reactor and accelerator neutrino experiments. The analysis is done for the three
flavor neutrino scenario, in the presence of matter and for general, noncyclic paths.
The geometric phase is seen to be sensitive to the CP violating phase in the leptonic
sector and the sign ambiguity in ∆31. We find that for experimental facilities where
the geometric phase can complete one cycle, all geometric phase curves corresponding
to different values of CP violating phase, converge to a single point, called the cluster
point. There are two distinct cluster points for positive and negative signs of ∆31. Thus
measurement of geometric phase in these experimental set-ups would help in resolving
the neutrino mass hierarchy problem (ref. [70]).
• We characterize Leggett-Garg-Type Inequality (LGtI) for three flavor neutrino oscil-
44
lations in the presence of matter and CP violating effects, showing how they can be
expressed in terms of the neutrino survival as well as oscillation probabilities. Hence,
our results are in terms of experimentally measurable quantities. We then explicitly
show the violation of LGtI in the context of two ongoing accelerator facilities, NOvA
and T2K. Remarkably, such combinations of two-time correlators are sensitive to the
well-known mass hierarchy problem in ∆31 and also to the CP violation in the leptonic
sector (ref. [71]).
• In this work we study temporal quantum correlations, quantified by Leggett-Garg (LG)
and LG-type inequalities, in the B and K meson systems. We use the tools of open
quantum systems to incorporate the effect of decoherence which is quantified by a
single phenomenological parameter. The effect of CP violation is also included in our
analysis. We find that the LG inequality is violated for both B and K meson systems,
the violation being most prominent in the case of K mesons and least for Bs system.
Since the systems with no coherence do not violate LGI, incorporating decoherence is
expected to decrease the extent of violation of LGI and is clearly brought out in our
results. We show that the expression for the LG functions depends upon an additional
term, apart from the experimentally measurable meson transition probabilities. This
term vanishes in the limit of zero decoherence. On the other hand, the LG-type
parameter can be directly expressed in terms of transition probabilities, making it a
more appropriate observable for studying temporal quantum correlations in neutral
meson systems (ref. [72]).
• Many facets of nonclassicality are probed in neutrino system in the context of three
flavour neutrino oscillations. The analysis is carried out for parameters relevant to two
ongoing experiments NOνA and T2K, and also for the upcoming experiment DUNE.
The various quantum correlations turn out to be sensitive to the mass-hierarchy prob-
lem in neutrinos. This sensitivity is found to be more prominent in DUNE experiment
45
as compared to NOνA and T2K experiments. This can be attributed to the large
baseline and high energy of the DUNE experiment. Further, we find that to probe
these correlations, the neutrino (antineutrino) beam should be preferred if the sign of
mass square difference ∆31 turns out to be positive (negative) (ref. [82]).
• Entropic Leggett-Garg inequality is studied in systems like neutrinos in the context
of two and three flavor neutrino oscillations and in neutral Bd, Bs and K mesons.
The neutrino dynamics is described with the matter effect taken into consideration.
For the decohering B/K meson systems, the effect of decoherence and CP violation
have also been taken into account, using the techniques of open quantum systems.
Enhancement in the violation with increase in the number of measurements has been
found, in consistency with findings in spin-s systems. The effect of decoherence is
found to bring the deficit parameter Dn closer to its classical value zero, as expected.
The violation of entropic Leggett-Garg inequality lasts for a much longer time in K
meson system than in Bd and Bs systems (ref. [83]).
• We study the interplay between coherence and mixedness in meson and neutrino sys-
tems. The dynamics of the meson system is treated using the open quantum system
approach taking into account the decaying nature of the system. Neutrino dynamics is
studied in the context of three flavor oscillations within the framework of a decoherence
model recently used in the context of LSND (Liquid Scintillator Neutrino Detector)
experiment. For meson systems, the decoherence effect is negligible in the limit of zero
CP violation. Interestingly, the average mixedness increases with time for about one
lifetime of these particles. For neutrino system, in the context of the model considered,
the decoherence effect is maximum for neutrino energy around 30 MeV. Further, the
effect of CP violating phase is found to decrease (increase) the coherence in the upper
0 < δ < π (lower π < δ < 2π) half plane (ref. [85]).
46
14 Particle Physics: Signatures of New Physics in the
Flavor Domain
• We consider a model where the standard model is extended by the addition of a vector-
like isosinglet down-type quark d′. We perform a χ2 fit to the flavor physics data
and obtain the preferred central values along with errors of all the elements of the
measurable 3×4 quark mixing matrix. We find that the data constrains |Vtb| ≥ 0.99 at
3σ. Hence, no large deviation in |Vtb| is possible, even if the mixing matrix is allowed to
be non-unitary. The fit also indicates that all the new-physics parameters are consistent
with zero, and the mixing of the d′ quark with the other three is constrained to be
small (ref. [58]).
• The VuQ (vector-singlet up-type quark) model involves the addition of a vector isos-
inglet up-type quark to the standard model. In this model the full CKM quark mixing
matrix is 4 × 3. Using present flavor-physics data, we perform a fit to this full CKM
matrix, looking for signals of new physics (NP). We find that the VuQ model is very
strongly constrained. There are no hints of NP in the CKM matrix, and any VuQ con-
tributions to loop-level flavor-changing b → s, b → d and s → d transitions are very
small. There can be significant enhancements of the branching ratios of the flavor-
changing decays t→ uZ and t→ cZ, but these are still below present detection levels
(ref. [59, 3]).
15 Quantum Optics and Quantum Information
• We study number-phase uncertainty in a laser-driven, effectively four-level atomic sys-
tem under electromagnetically induced transparency (EIT) and coherent population
trapping (CPT). Uncertainty is described using (entropic) knowledge of the two com-
plementary variables, namely, number and phase, where knowledge is defined as the
relative entropy with respect to a uniform distribution. The noise produced by ramp-
47
ing the probe off-resonance is studied in the cases with and without a higher order
nonlinearity due to a 3 − 4′ transition. In both cases, the noise is consistent with
purely dephasing action in the number basis in the CPT as well as EIT regimes. Our
study leads us to the following novel results: We see as a consequence of number-phase
complementarity that the dipole oscillations are correlated in the CPT state, and that
this correlation drops as EIT is approached. The cooperative change in phase with
zero absorption, of coherent light, in a medium formed by atoms in a CPT state can
result in generation of new frequencies whose width depends on amount of cooperation.
The power spectrum of the generated frequencies will depend on whether the atoms
are in CPT or EIT state. Our predictions can explain a recent experimental study.
The Complementarity approach taken easily brings out this difference in CPT and
EIT and helps understand the result our study shows regarding the effect of inclusion
of higher order nonlinearities. We show their presence is detrimental for cooperative
behaviour. Our nonlinear system has properties parallel to the system modelled earlier
by Manassah et. al., and hence can show superradiance. The advantage in our system
is that it is amenable to experiments. CPT and EIT can thus be used in a novel way
to bring about a change in the photon statistics of laser light (ref.[33]).
• Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric
phase corresponding to the radiation emitted by a three level cascade system pro-
vides a sensitive diagnostic tool for determining the entanglement properties of the
two modes of radiation. The nonunitary, noncyclic path in the state space may be
realized through the same control parameters which control the purity/mixedness and
entanglement. We show that the rate of change of the geometric phase reveals its
resilience to fluctuations only for pure Bell type states (ref.[32]).
• The nonclassicality of the two mode photon state generated in a semiclassical, gen-
eralized three-level atomic system, interacting with classical external driving fields is
48
investigated. The three-level system is considered in any one of the Ξ, Λ or V con-
figuration. The nonclassicality of these two-mode photons can be investigated using
measurement based nonclassical correlations such as measurement induced disturbance,
uantum discord and quantum work deficit. We compare the behavior of these mea-
sures with entanglement (concurrence) and analyze the correlation dynamics at specific
system parameter regimes based on broad observation. We observe, that the qualita-
tive nature of hierarchy of the correlations is dependent on the specificied regime and
configuration. Based on the observations, we comment on how particular configura-
tions are better suited at generating monotonic orrelations at specific regimes and how
the correlation behavior and hierarchy is affected by the population dymanics of the
density matrix (ref. [38]).
• We study nonclassical features in a number of spin-qubit systems including single, two
and three qubit states, as well as an N qubit Dicke model and a spin-1 system, of
importance in the fields of quantum optics and information. This is done by analyzing
the behavior of the well known Wigner, P , and Q quasiprobability distributions on
them. We also discuss the not so well known F function and specify its relation to
the Wigner function. Here we provide a comprehensive analysis of quasiprobability
distributions for spin-qubit systems under general open system effects, including both
pure dephasing as well as dissipation. This makes it relevant from the perspective of
experimental implementation (ref. [51]).
• Tomograms are obtained as probability distributions and are used to reconstruct a
quantum state from experimentally measured values. We study the evolution of tomo-
grams for different quantum systems, both finite and infinite dimensional. In realistic
experimental conditions, the quantum states are exposed to the ambient environment
and hence subject to effects like decoherence and dissipation, which are dealt with here,
consistently, using the formalism of open quantum systems. This is extremely relevant
49
from the perspective of experimental implementation and issues related to state re-
construction in quantum computation and communication. These considerations are
also expected to affect the quasiprobability distribution obtained from experimentally
generated tomograms and nonclassicality observed from them (ref. [52]).
• The possibility of observing nonclassical features in a physical system comprised of
a cavity with two ensembles of two-level atoms has been investigated by considering
different configurations of the ensembles with respect to the Node and Antinode of
the cavity field under the framework of open quantum systems. The study reveals the
strong presence of nonclassical characters in the physical system by establishing the
existence of many facets of nonclassicality, such as the sub-Poissonian boson statis-
tics and squeezing in single modes, intermodal squeezing, intermodal entanglement,
antibunching, and steering. The effect of a number of parameters, characterizing the
physical system, on the different aspects of nonclassicality are also investigated. Specif-
ically, it is observed that the depth of the nonclassicality witnessing parameters can be
enhanced by externally driving one of the ensembles with an optical field. The work
is done in the presence of open system effects, in particular, use is made of Langevin
equations along with a suitable perturbative technique (ref. [79]).
• Nonclassical properties of photon added and subtracted displaced Fock states have
been studied using various witnesses of lower- and higher-order nonclassicality. Com-
pact analytic expressions are obtained for the nonclassicality witnesses. Using those
expressions, it is established that these states and the states that can be obtained as
their limiting cases (except coherent states) are highly nonclassical as they show the
existence of lower- and higher-order antibunching and sub-Poissonian photon statistics,
in addition to the nonclassical features revealed through the Mandel QM parameter,
zeros of Q function, Klyshko’s criterion, and Agarwal-Tara criterion. Further, some
comparison between the nonclassicality of photon added and subtracted displaced Fock
50
states have been performed using witnesses of nonclassicality. This has established that
between the two types of non-Gaussianity inducing operations (i.e., photon addition
and subtraction) used here, photon addition influences the nonclassical properties more
strongly. Further, optical designs for the generation of photon added and subtracted
displaced Fock states from squeezed vacuum state have also been proposed (ref. [84]).
16 Quantum Games
• We present a new form of a Parrondo game using discrete-time quantum walk on a
line. The two players A and B with different quantum coins operators, individually
losing the game can develop a strategy to emerge as joint winners by using their coins
alternatively, or in combination for each step of the quantum walk evolution. We also
present a strategy for a player A (B) to have a winning probability more than player B
(A). Significance of the game strategy in information theory and physical applications
are also discussed (ref.[29]).
17 Non-Linear Dynamics
• A new q-deformed logistic map is proposed and it is found to have concavity in parts of
the x-space. Its one-cycle and two-cycle non-trivial fixed points are obtained which are
found to be qualitatively and quantitatively different from those of the usual logistic
map. The stabilty of the proposed q-logistic map is studied using Lyapunov exponent
and with a change in the value of the deformation parameter q, one is able to go from
the chaotic to regular dynamical regime. The implications of this q-logistic map on
Parrondo’s paradox are examined (ref.[25]).
• The delay logistic map with two types of q–deformations: Tsallis and Quantum–group
type are studied. The stability of the map and its bifurcation scheme is analyzed as a
function of the deformation and delay feedback parameters. Chaos is suppressed in a
certain region of deformation and feedback parameter space. The steady state obtained
51
by delay feedback is maintained in one type of deformation while chaotic behavior is
recovered in another type with increasing delay (ref.[34]).
18 Generalized Thermodynamics
• We investigate the most general meaning of intrinsic Riemannian geometry for com-
plex systems from the perspective of statistical mechanics and associated probability
distributions. The entropic formulation of statistical mechanics is the ingredient which
enables a connection between statistical mechanics and the corresponding Riemannian
geometry. The form of the entropy used commonly is the Shannon entropy. How-
ever, for modelling complex systems it is often useful to make use of higher entropies
such as the Renyi and Tsallis entropies. We consider Shannon, Renyi and Tsallis en-
tropies for our analysis. We focus on the one, two and the three particle thermally
excited configurations. We find that statistical pair correlation functions associated
with Gibbs-Shannon, Renyi and Tsallis configurations have well defined definite ex-
pressions, which may be extended for arbitrary finite particle systems. In either case,
we find a well defined intrinsic Remannian manifold. In particular, any finite particle
Renyi and Tsallis configurations always correspond to an interacting statistical sys-
tem. On the other hand, the Gibbs-Shannon system corresponds to a non-interactiing
statistical configuration. Moreover, the underlying statistical configurations associated
with Renyi and Tsallis systems become ill-defined at the extreme value of the Renyi
parameter, q = 1 while the Gibbs-Shannon remains intact (ref.[36]).
• It is found that Tsallis and Renyi entropies are suited in modeling complex systems
where long range correlations play an important role in a description of the system
dynamics. These entropies form a q generalization of the well known Shannon entropy
to which they reduce to in the limit of q −→ 1. The q serves as a scaling parameter en-
abling the system to sample, not necessarily, neighbouring points. These issues are inti-
mately connected to quantum groups. Here we propose a two-parameter generalization
52
of these entropies, to which they reduce to in the limit of one of the parameters tending
to one. The basic tool is a two-parameter difference operator acting on an appropriate
generating function. From this one attains a family of generalized entropies including
a two-parameter generalization of the Renyi entropy. Taking appropriate limits, many
other entropies known in the literature are recovered. From the two-parameter Renyi
one can recover the two-parameter Tsallis entropy by expanding the logarithmic terms
in the Renyi entropy and keeping only the linear term. This two-parameter difference
operator has its origin in the corresponding two-parameter generalization of quantum
groups. We make a number of applications of these generalized entropies (ref.[37]).
Publications: Journal Publications
1. “Quantum theory of a Stern-Gerlach system in contact with a lineraly dissipative
environment”
S. Banerjee and R. Ghosh, Physical Review A: 62, 042105 (2000).
2. “Propagator for a spin-Bose system with the Bose field coupled to a reservoir of har-
monic oscillators”
S. Banerjee and R. Ghosh, J. Phys. A: Math. Gen: 36, 5787 (2003).
3. “General quantum Brownian motion with initially correlated and nonlineraly coupled
environment”
S. Banerjee and R. Ghosh, Physical Review E.: 67, 056120 (2003).
4. “Decoherence and dissipation of an open quantum system with a squeezed and fre-
quency modulated heat bath”
S. Banerjee, Physica A: 337, 67 (2004).
5. “Ultracoherence and Canonical Transformations”
J. Kupsch and S. Banerjee, Infinite Dimensional Analysis, Quantum Probability and
Related Topics: 9, 413 (2006), eprint: arXiv:math-ph/0410049.
53
6. “Applications of Canonical Transformations”
S. Banerjee and J. Kupsch, J. Phys. A: Math. Gen 38, 5237 (2005), eprint: arXiv:quant-
ph/0410209.
7. “Structure of Propagators for quantum nondemolition systems”
S. Banerjee and R. Ghosh, eprint: arXiv:quant-ph/0611125.
8. “Functional integral treatment of some quantum nondemolition systems and their vari-
ants”
S. Banerjee and R. Ghosh, J. Phys. A: Math. Theo.: 40, 1273 (2007), eprint:arXiv:quant-
ph/0611127.
9. “Dynamics of decoherence without dissipation in a squeezed thermal bath”
S. Banerjee and R. Ghosh, J. Phys. A:Math. Theo: 40, 13735 (2007), eprint:
arXiv:quant-ph/0703054.
10. “Classical limit of master equation for harmonic oscillator coupled to oscillator bath
with separable initial conditions”
S. Banerjee and A. Dhar, Physical Review E: 73, 067104 (2006), eprint: arXiv:cond-
mat/0511645.
11. “Phase diffusion pattern in quantum nondemolition systems”
S. Banerjee, J. Ghosh and R. Ghosh, Phys. Rev. A: 75, 062106 (2007), eprint:arXiv:quant-
ph/0703055.
12. “Geometric Phase of a qubit interacting with a squeezed-thermal bath”
S. Banerjee and R. Srikanth, Eur. Phys. J. D: 46, 335 (2008), eprint: arXiv:quant-
ph/0611161.
13. “An environment-mediated quantum deleter”
R. Srikanth and S. Banerjee, Phys. Lett. A: 367, 295 (2007), eprint: arXiv:quant-
ph/0611263.
54
14. “ Phase diffusion in quantum dissipative systems”
S. Banerjee and R. Srikanth, Phys. Rev. A: 76, 062109 (2007), eprint:arXiv:0706.3633.
15. “ Complementarity in atomic systems: an information-theoretic approach”
R. Srikanth and S. Banerjee, Eur. Phys. J. D: 53, 217 (2009), eprint: arXiv:0711.0875.
16. “Complementarity in generic open quantum systems”
S. Banerjee and R. Srikanth, Modern Phys. Lett. B: 24, 2485 (2010), eprint: arXiv:0905.3269.
17. “Complementarity in atomic and oscillator systems”
R. Srikanth and S. Banerjee, Phys. Lett. A: 374, 3147 (2010), eprint:arXiv: 1005.3456.
18. “ Symmetries and noise in quantum walk”
C. M. Chandrashekar, R. Srikanth and S. Banerjee, Phys. Rev. A: 76, 022316 (2007),
eprint: arXiv:quant-ph/0607188.
19. “Symmetry-noise interplay in quantum walk on n-cycle”
S. Banerjee, R. Srikanth, C. M. Chandrashekar and Pranaw Rungta, Phys. Rev. A:
78, 052316 (2008), eprint: arXiv:0803.4453.
20. “ The squeezed generalized amplitude damping channel”
R. Srikanth and S. Banerjee, Phys. Rev. A: 77, 012318 (2008), eprint:arXiv:0707.0059.
21. “Entanglement dynamics in two-qubit open quantum system interacting with a squeezed
thermal bath via quantum nondemolition interaction”
S. Banerjee, V. Ravishankar and R. Srikanth, Euro. Phys. J. D: 56, 277 (2010),
eprint:arXiv:0810.5034.
55
22. “ Dynamics of entanglement in two-qubit open quantum system interacting with a
squeezed thermal bath via dissipative interaction”
S. Banerjee, V. Ravishankar, R. Srikanth, Ann. of Phys. (NY).: 325, 816 (2010),
eprint:arXiv:0901.0404 .
23. “Geometric phase in a two-qubit system interacting with a bath via quantum non-
demolition as well as dissipative interactions”
S. Banerjee and R. Srikanth, work in progress.
24. “Relationship Between Quantum Walk and Relativistic Quantum Mechanics”
C. M. Chandrashekar, S. Banerjee and R. Srikanth, Phys. Rev. A: 81, 062340 (2010),
eprint: arXiv:1003.4656.
25. “A q-deformed logistic map and its implications”
S. Banerjee and R. Parthasarathy, J. Phys. A.:Math. Theor.: 44, 045104 (2011),
eprint:arXiv:1003.0183.
26. “A study of Quantum Correlations in Open Quantum Systems”
I. Chakrabarty, S. Banerjee and N. Siddharth, Quantum Information and Computation:
11, 0541 (2011), eprint:arXiv:1006.1856.
27. “Quantumness in decoherent quantum walk using measurement-induced disturbance”
R. Srikanth, S. Banerjee and C. M. Chandrashekar, Phys. Rev. A: 81, 062123 (2010),
eprint:arXiv:1005.3456.
28. “Entanglement generation in spatially separated systems using quantum walk”
C. M. Chandrashekar, S. K. Goyal and S. Banerjee, Journal of Quantum Information
Science: 2, 15 (2012), eprint:arXiv:1005.3785.
29. “Parrondo’s game using a discrete-time quantum walk”
C. M. Chandrashekar and S. Banerjee, Phys. Lett. A: 375, 1553 (2011), arXiv:1008.5121.
56
30. “Quantumness of noisy quantum walks: a comparison between measurement-induced
disturbance and quantum discord”
B. R. Rao, R. Srikanth, C. M. Chandrashekar and S. Banerjee, Phys. Rev. A: 83,
064302 (2011), eprint:arXiv:1012.5040.
31. “Effect of control procedures on the evolution of entanglement in open quantum sys-
tems”
S. Goyal, S. Banerjee and S. Ghosh, Phys. Rev. A: 85, 012327 (2012), eprint:arXiv:1102.4403.
32. “Geometric Phase: An Indicator of Entanglement”
S. N. Sandhya and S. Banerjee, Euro. Phys. J. D: 66, 168 (2012), eprint:arXiv:1103.2587.
33. “An information theoretic study of number-phase uncertainty in a four level atomic
system”
A. Sharma, R. Srikanth, S. Banerjee and H. Ramachandran, arXiv:1108.0641.
34. “q–deformed logistic map with delay feedback”
M. D. Shrimali and S. Banerjee, arXiv:1203.3137; Commun. Nonlinear Sci. Numer.
Simulat (CNSNS) 18, 3126 (2013).
35. “The quantum cryptographic switch”
S Narayanaswamy, O Srikrishna, R Srikanth, S. Banerjee and A. Pathak, arXiv:1111.4834;
Quantum Information Processing, Special Issue on Quantum Cryptography 13, 59
(2014).
36. “A thermodynamic geometric study of Renyi and Tsallis entropies”
B. N. Tiwari, V. Chandra and S. Banerjee, arXiv:1008.2853.
37. “A family of generalized entropies”
R. Jagannathan and S. Banerjee, work in progress.
57
38. “Investigating nonclassical correlations of radiation emitted from generalized three-
level atomic systems”
H. S. Dhar, S. Banerjee, A. Chatterjee and R. Ghosh, Ann. of Phys. 331, 97 (2013),
arXiv:1205.5665.
39. “Laplacian matrices of weighted digraphs represented as quantum states”, Quantum
Information Processing 16, 1-22 (2017) : Eprint:arXiv:1205.2747: Bibhas Adhikari,
Subhashish Banerjee, Satyabrata Adhikari and Atul Kumar.
40. “Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry”
S. Omkar, R. Srikanth and S. Banerjee, Quantum Information Processing 12, 3725
(2013), arXiv:1207.7226.
41. “An Operational Meaning of Discord in terms of Teleportation Fidelity”
S. Adhikari and S. Banerjee, Phys. Rev. A 86, 062313 (2012), arXiv:1207.7226.
42. “Quantification of Entanglement of Teleportation in Arbitrary Dimensions”
Sk Sazim, S. Adhikari, S. Banerjee and T. Pramanik, Quantum Information Processing
13, 863 (2014), arXiv:1208.4200.
43. “Enhancement of Geometric Phase by Frustration of Decoherence: A Parrondo like
Effect”
S. Banerjee, C. M. Chandrashekar and A. K. Pati, Phys. Rev. A 87, 042119 (2013),
arXiv:1208.5563.
44. “The operator sum-difference representation for quantum maps: application to the
two-qubit amplitude damping channel”
S. Omkar, R. Srikanth and S. Banerjee, Quantum Information Processing 14, 2255
(2015), doi:10.1007/s11128-015-0965-5, arXiv:1212.2780.
45. “Decoherence free B d and B s meson systems”
A. K. Alok and S. Banerjee, Phys. Rev. D 88, 094013 (2013), arXiv:1304.4063.
58
46. “Entanglement in the Grovers Search Algorithm” S. Chakraborty, S. Banerjee, S. Ad-
hikari and A. Kumar, arXiv:1305.4454.
47. “Quantum code for quantum error characterization”, S. Omkar, R. Srikanth and S.
Banerjee, Phys. Rev. A 91, 052309 (2015).
48. “Characterization of quantum dynamics using quantum error correction”, S. Omkar,
R. Srikanth and S. Banerjee, Phys. Rev. A 91, 012324 (2015), Eprint:arXiv:1405.0964.
49. “A graph theoretical approach to states and unitary operations”, Quantum Information
Processing 15, 2193 (2016); Eprint:arXiv:1502.07821: Supriyo Dutta, Bibhas Adhikari,
Subhashish Banerjee.
50. “Controlled bidirectional remote state preparation in noisy environment: A generalized
view”, Quantum Information Processing 14, 3441 (2015), doi:10.1007/s11128-015-1038-
5: Eprint:arXiv:1492.0833: V. Sharma, C. Shukla, S. Banerjee and A. Pathak.
51. “Quasiprobability distributions in open quantum systems: spin-qubit systems”, Ann.
of Phys. 362, 261286 (2015), Kishore Thapliyal, Subhashish Banerjee, Anirban Pathak,
S. Omkar, V. Ravishankar.
52. “Tomograms for open quantum systems: in(finite) dimensional optical and spin sys-
tems”: Ann. of Phys. 366, 148 (2016); arXiv:1507.02135: Kishore Thapliyal, Sub-
hashish Banerjee, Anirban Pathak.
53. “The Unruh effect interpreted as a quantum noise channel”, Quantum Information and
Computation (QIC) 16, 0757 (2016); Eprint:arXiv:1408.1477: S. Omkar, S. Banerjee,
R. Srikanth and A. K. Alok.
54. “Quantum correlations in B and K meson systems”, Eur. Phys. J. Plus 131, 129
(2016); Eprint:arXiv:1409.1034: S. Banerjee, A. K. Alok and R. MacKenzie.
59
55. “Quantum correlations in two-flavor neutrino oscillations”, Nucl. Phys. B 909, 65
(2016); Eprint:arXiv:1411.5536: A. K. Alok, S. Banerjee and S. U. Sankar.
56. “A quantum information theoretic analysis of three flavor neutrino oscillations”: Euro-
pean Physical Journal C (EPJC) 75, 487 (2015); arXiv:1508.03480: Subhashish Baner-
jee, Ashutosh Kumar Alok, R. Srikanth and Beatrix C. Hiesmayr.
57. “Re-examining sin(2beta) and Delta m(d) from evolution of B(d) mesons with deco-
herence”, Phys. Lett. B 749, 94 (2015): Ashutosh Kumar Alok, Subhashish Banerjee
and S. Uma Sankar.
58. “Constraining quark mixing matrix in isosinglet vector-like down quark model from a
fit to flavor-physics data”, Nucl. Phys. B 906, 321 (2016); Eprint:arXiv:1402.1023: A.
K. Alok, S. Banerjee, D. Kumar and S. U. Sankar.
59. “New-physics signals of a model with a vector-singlet up-type quark”, Phys. Rev. D
92, 013002 (2015): Ashutosh Kumar Alok, Subhashish Banerjee, Dinesh Kumar, S.
Uma Sankar and David London.
60. “Quantum Fisher and Skew information for Unruh accelerated Dirac qubit”: Eur.
Phys. J. C (EPJC) 76, 437 (2016); arXiv:1511.03029: Subhashish Banerjee, Ashutosh
Kumar Alok and S. Omkar.
61. “The two-qubit amplitude damping channel: characterization using quantum stabilizer
codes”: Ann. of Phys. 373, 145 (2016); arXiv:1511.03368: S. Omkar, R. Srikanth,
Subhashish Banerjee and Anil Shaji.
62. “Evolution of coherence and non-classicality under global environmental interaction ”:
Quantum Information Processing 17, 236 (2018); arXiv:1601.04742: Samyadeb Bhat-
tacharya, Subhashish Banerjee and Arun Kumar Pati.
60
63. “Bipartite separability and non-local quantum operations on graphs ”: Phys. Rev.
A 94, 012306 (2016); arXiv:1601.07704: Supriyo Dutta, Bibhas Adhikari, Subhashish
Banerjee and R. Srikanth.
64. “A comparative study of protocols for secure quantum communication under noisy en-
vironment: single-qubit-based protocols versus entangled-state-based protocols”: Quan-
tum Information Processing 15, 4681 (2016), DOI 10.1007/s11128-0016-1396-7; arXiv:1603.00178:
Vishal Sharma, Kishore Thapliyal, Anirban Pathak and Subhashish Banerjee.
65. “Characterization of Unruh Channel in the context of Open Quantum Systems”: Jour-
nal of High Energy Physics (JHEP) 02, 82 (2017), DOI: 10.1007/JHEP02(2017);
arXiv:1603.05450: Subhashish Banerjee, Ashutosh Kumar Alok, S. Omkar and R.
Srikanth.
66. “Quantum cryptography over non-Markovian channels”: Quantum Information Pro-
cessing, 16, 115 (2017), DOI: 10.1007/s11128-017-1567-1; arXiv:1608.06071: Kishore
Thapliyal, Anirban Pathak and Subhashish Banerjee.
67. “Seidel switching for weighted multi-digraphs and its quantum perspective”: arXiv:1608.07830:
Supriyo Dutta, Bibhas Adhikari and Subhashish Banerjee.
68. “Quantum discord of states arising from graphs” Quantum Information Processing,
16(8), 183 (2017), arXiv:1702.06360: Supriyo Dutta, Bibhas Adhikari, Subhashish
Banerjee.
69. “Zero discord quantum states arising from weighted digraphs”: arXiv:1705.00808:
Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee.
70. “Geometric phase and neutrino mass hierarchy problem”: J. Phys. G, 45, 085002
(2018), arXiv:1703.09894: Khushboo Dixit, Ashutosh Kumar Alok, Subhashish Baner-
jee and Dinesh Kumar.
61
71. “Legget-Garg-Type inequalities and the neutrino mass-degeneracy problem”: arXiv:1710.05562:
Javid Naikoo, Ashutosh Kumar Alok, Subhashish Banerjee, S. Uma Sankar, Giacomo
Guarnieri and Beatrix C. Hiesmayr.
72. “Study of temporal quantum correlations in decohering B and K meson systems”:
Phys. Rev. D 97, 053008 (2018); arXiv:1802.04265: Javid Naikoo, Ashutosh Kumar
Alok, Subhashish Banerjee.
73. “Non-Markovian Dynamics of Discrete-Time Quantum Walks”: arXiv:1703.08004: Sub-
hashish Banerjee, N. Pradeep Kumar, R. Srikanth, Vinayak Jagadish and Francesco
Petruccione.
74. “Non-Markovian evolution: a quantum walk perspective”: Open Systems and Infor-
mation Dynamics (OSID) 25, 1850014 (2018); arXiv:1711.03267: Pradeep Kumar,
Subhashish Banerjee, R. Srikanth, Vinayak Jagadish and Francesco Petruccione.
75. “Thermodynamics of non-Markovian reservoirs and heat engines”: Phys. Rev. E
97, 062108 (2018): arXiv:1801.00744v1: George Thomas, Nana Siddharth, Subhashish
Banerjee and Sibasish Ghosh. .
76. “Enhanced non-Markovian behavior in quantum walks with Markovian disorder”: Sci-
entific Reports 8, 8801 (2018); DOI:10.1038/s41598-018-27132-7arXiv:1802.05478: arXiv:1802.05478:
N. Pradeep Kumar, Subhashish Banerjee and C. M. Chandrashekar.
77. “Analysis of atmospheric effects on satellite based quantum communication: A com-
parative study”: arXiv:1711.08281: Vishal Sharma and Subhashish Banerjee.
78. “Decoherence can help quantum cryptographic security”: Quantum Information Pro-
cessing, 17, 207 (2018), arXiv:1712.06519: Vishal Sharma, U. Shrikant, R. Srikanth
and Subhashish Banerjee.
62
79. “Probing nonclassicality in an optically-driven cavity with two atomic ensembles”:
Phys. Rev. A 97, 063840 (2018); arXiv:1712.04154: Javid Naikoo, Kishore Thapliyal,
Anirban Pathak and Subhashish Banerjee.
80. “Non-Markovian dephasing and depolarizing channels”: Phys. Rev. A 98, 032328
(2018); arXiv:1805.11411: U. Shrikant, R. Srikanth and Subhashish Banerjee.
81. “Leggett-Garg inequality violation under non-Markovian noise”: arXiv:1806.00537:
Javid Naikoo, Subhashish Banerjee and R. Srikanth.
82. “Quantum correlations and the neutrino mass degeneracy problem”: Eur. Phys. J. C
78, 914 (2018), arXiv:1807.01546: Khushboo Dixit, Javid Naikoo, Subhashish Banerjee
and Ashutosh Kumar Alok.
83. “Entropic Leggett-Garg inequality in neutrinos and B (K) meson systems”: Eur. Phys.
J. C 78, 602 (2018): Javid Naikoo and Subhashish Banerjee.
84. “Lower- and higher-order nonclassical properties of photon added and subtracted dis-
placed Fock states”: arXiv:1808.01458: : accepted for publication in Annalen der
Physik; Priya Malpani, Nasir Alam, Kishore Thapliyal, Anirban Pathak, V. Narayanan
and Subhashish Banerjee.
85. “Study of coherence and mixedness in meson and neutrino systems”: arXiv:1809.09947:
Khushboo Dixit, Javid Naikoo, Subhashish Banerjee and Ashutosh Kumar Alok.
Publications: Conference Publications
1. “An Invitation to Open Quantum Systems Applied to Quantum Information” S. Baner-
jee, Proceedings of National Conference on Quantum Correlations: Foundations and
Applications, organized by Department of Physics, Vidyasagar College for Women,
Kolkata along with Physics and Applied Mathematics Unit, Indian Statistical Insti-
tute, Kolkata .
63
2. “Effect of decoherence on clean determination of sin(2β) and ∆md” Ashutosh Kumar
Alok, Subhashish Banerjee and S. Uma Sankar; PoS (Proceedings of Science) EPS-
HEP2015 (2015) 578 .
3. “New-physics signals of a model with an isosinglet vector-like t′ quark” Ashutosh Ku-
mar Alok, Subhashish Banerjee, Dinesh Kumar, S. Uma Sankar and David London;
PoS (Proceedings of Science) EPS-HEP2015 (2015) 579 .
4. “Analysis of Quantum Key Distribution based Satellite Communication” Vishal Sharma,
Subhashish Banerjee; in 2018 9th International Conference on Computing, Communi-
cation and Networking Technologies (ICCCNT) 2018 Jul 10 (pp. 1-5). IEEE, DOI:
10.1109/ICCCNT.2018.8494189.; arXiv:1807.07544.
Publications: Book Chapters
1. “Principles and Applications of Free Space Optical Communica tion”, Authors: Vishal
Sharma, Subhashish Banerjee and Bazil Raj; ISBN: 978-1-78561-415-6 (https://www.theiet.org/resources/books/telecom/free-
space.cfm).
Publications: Monographs
1. A Thermodynamic Geometric Study of Complex Entropies
B. N. Tiwari, V. Chandra and S. Banerjee, Lap Lambert Academic Publishing (2011).
2. A Study of Dynamics of Open Quantum Systems
S. Banerjee, Lap Lambert Academic Publishing (2011).
Publications: Books
1. Open Quantum Systems: Dynamics of Nonclassical Evolution
Subhashish Banerjee, Springer and Hindustan Book Agency; ISBN 978-981-13-3181-7,
ISBN 978-981-13-3182-4 (eBook), https://doi.org/10.1007/978-981-13-3182-4.
64
Awards:
Awarded the “Science Foundation Ireland Short Term Travel Fellowship” from May 1 2012
to July 31 2012.
Projects:
(a). Co-Principal Investigator in the CSIR funded project on “Hunting of new physics
through b→ s transitions”. Project completed;;
(b). Principal Investigator in the CSIR funded project on “Graph Theoretical Aspects in
Quantum Information Processing”. Project completed;
(c). Principal Investigator in the CSIR funded project on “A Study of Quantum Correlations:
Squeezing and its various facets”. Project ongoing;
(d). Principal Investigator, from the Indian side, in the “DST India-BMWfW Austria Project
Based Personnel Exchange Programme for 2017-2018”, titled “Probing the Foundations of
Quantum Mechanics in Neutrino Oscillations”. Project ongoing.
Students:
A. Undergraduate:
1. Guided B. Tech. Project of Jothishwaran C. Arunagiri, IIT Jodhpur, titled “Towards
a better understanding of the Josephson Qubits” (2013);
2. Guided B. Tech. Project of Amar Singh Saini, IIT Jodhpur, titled “Quantum Cryp-
tography (Quantum Repeater Technology)” (2014);
3. Guided Summer Internship Project of Ravi and Pradeep Saran, IISER Bhopal, titled
“Quantum Computing and Information” (2014).
B. Postgraduate:
1. Guided the Masters (M.Tech.) Thesis of Shantanav Chakraborty, IIT Jodhpur, titled
“Entanglement in the Quantum Search Algorithm”.
2. Guided the MSc Thesis of Nidhin Sathyan, IIT Jodhpur, titled “Studies on Quantum
65
Entanglement”.
3. Guided the M.Tech training project for 8 th semester MSc Thesis of Vikrant Chaud-
hary, IIT Jodhpur, titled “Photon Localization”.
4. Guided the M.Tech training project for 8 th Semester of Komal Varshney, a student
of B.Tech - M.Tech 4 th year at Centre for Converging Technologies, University of
Rajasthan (UOR), Jaipur titled Quantum Cryptography.
C. Ph.D:
1. Vibha Sahlot: Thesis submitted. Thesis title “Conflicts in Geometry”.
2. Supriyo Dutta: Thesis submitted. Thesis title “Graph Theoretic Aspects of Quantum
Information Processing”.
3. Vishal Sharma: Thesis submitted. Thesis title “Quantum communication under noisy
environment: from Theory to Applications”.
4. Javid Ahmad Naikoo: Thesis ongoing.
Additional:
(a). Invited reviewer for Mathematical Reviews (MR);
(b). Reviewer for J. of Stat. Phys;
(c). Reviewer for J. Phys. A;
(d). Reviewer for J. Phys. B;
(e). Reviewer for Physica A;
(f). Reviewer for QIC and QIP;
(g). Reviewer for Pramana;
(h). Reviewer for Phys. Rev. A;
66
(i). Reviewer for Phys. Rev. D.
(j). Reviewer of two thesis.
67