Implementation of Practically Secure Implementation of Practically Secure Quantum Bit Commitment ProtocolQuantum Bit Commitment Protocol

Ariel Danan Ariel Danan

School of Physics Tel Aviv UniversitySchool of Physics Tel Aviv University

September 2008September 2008

Project Members:Project Members: Ariel Danan, Yoav LinzonAriel Danan, Yoav Linzon(With a lot of help from Ezra Shaked- electronic workshop)(With a lot of help from Ezra Shaked- electronic workshop)

Academic supervisors:Academic supervisors: Lev Vaidman and Shimshon BaradLev Vaidman and Shimshon Barad

OutlineOutline Introduction Introduction Bit CommitmentBit Commitment Practically Secure Quantum Bit CommitmentPractically Secure Quantum Bit Commitment Phase Encoding with Optical FibersPhase Encoding with Optical Fibers Experimental SetupExperimental Setup Demonstration (Q.O. lab)Demonstration (Q.O. lab) Security Discussion Security Discussion Final ResultsFinal Results Future ProspectsFuture Prospects

IntroductionIntroduction Quantum Information Quantum Information →→ Quantum computers Quantum computers

((Grover's quantum searchGrover's quantum search , , Shor's quantum factoringShor's quantum factoring ….)….) Quantum Key Distribution Quantum Key Distribution ↔↔ ‘No Cloning Theorem’ ‘No Cloning Theorem’

Unconditionally Secure Quantum Bit Commitment Unconditionally Secure Quantum Bit Commitment →→ ‘No Go Theorem’ ‘No Go Theorem’ Practically Secure Quantum Bit CommitmentPractically Secure Quantum Bit Commitment

Based on the limitation of current technologiesBased on the limitation of current technologies(Non-demolition measurement and long quantum memory)(Non-demolition measurement and long quantum memory)

IntroductionIntroduction

Lev’s Practically Secure Quantum Bit Commitment ProtocolLev’s Practically Secure Quantum Bit Commitment ProtocolPatent Pending Patent Pending →→ The term Non Demolition measurement was not used The term Non Demolition measurement was not used

in the thesis in the thesis

Implementation of Practically Secure Quantum Bit Commitment using low Implementation of Practically Secure Quantum Bit Commitment using low cost quantum optics devicescost quantum optics devices

What is Bit Commitment?What is Bit Commitment? Committing phase:Committing phase: Alice select a bit, put it in a strong box and sends it to Bob Alice select a bit, put it in a strong box and sends it to Bob

0 1or

Bob

Alice

Opening Phase:Opening Phase: Alice sends the key to Bob and he reveals her commitmentAlice sends the key to Bob and he reveals her commitment

Alice

10 or

Bob

Both Classical and Quantum Unconditionally Secure bit Both Classical and Quantum Unconditionally Secure bit commitment is impossible!commitment is impossible!

ApplicationsApplications Secure Commercial BidingSecure Commercial Biding

User AuthenticationUser Authentication

Lon distance coin TossingLon distance coin Tossing

Oblivious Transfer Oblivious Transfer (Two party secure computation)(Two party secure computation)

רק לא גיידאמק!

#@

?אתמול היה

לי יותר

Conjugate observablesConjugate observables

Photon has 2 bases of polarization that don’t commute. Photon has 2 bases of polarization that don’t commute.

Rectilinear basis:eigenstates of σz

Diagonal basis:eigenstates of σx

Practical secure QBC protocolPractical secure QBC protocolCommitting phase:Committing phase: Bob sends photons prepared randomly in one of the 4 polarization Bob sends photons prepared randomly in one of the 4 polarization

{ } to Alice.{ } to Alice. Bob keeps the record of when and what he sent to Alice.Bob keeps the record of when and what he sent to Alice. Alice measures all photons in one of two bases which manifests her Alice measures all photons in one of two bases which manifests her

commitment { } = commitment { } = 00 { } = { } = 11.. She announces immediately the time of detection of the photons.She announces immediately the time of detection of the photons.

BobAlice

b =0or

b =1

Pulse No. 1045 Pulse No. 1045 (1,1)

Pulse No. 1044 (0,1)

Pulse No. 1043 (1,1)

Pulse No. 1042 (0,0)

OpeningOpening PhasePhase::-Alice reveals her commitment (measurement base) and the measurements Alice reveals her commitment (measurement base) and the measurements outcomes.outcomes.

--Bob checks Alice’s answers.Bob checks Alice’s answers.

BobAlice

AdvantagesAdvantages

1.1. Cheating tasks (long-time Qubit memory, Perfect Non-Cheating tasks (long-time Qubit memory, Perfect Non-demolition Measurement) are beyond current technologydemolition Measurement) are beyond current technology

2.2. No need for high fidelity (the security increase exponential No need for high fidelity (the security increase exponential with the number of Qubits per commitment).with the number of Qubits per commitment).

3.3. Short distances possibility (unlike Classical bit Short distances possibility (unlike Classical bit commitment)commitment)

4.4. Since Alice don’t control the information she gets, it’s more Since Alice don’t control the information she gets, it’s more difficult for her to cheat.difficult for her to cheat.

5.5. BobBob cannot gain information about cannot gain information about AliceAlice's commitment or 's commitment or measurements outcomes before she announces them. measurements outcomes before she announces them.

Phase Encoding with Optical FibersPhase Encoding with Optical Fibers

SentQubitΦ1Φ2

Meas.BasisD0D1

0,0025%0%

1,0012.5%12.5%

0,100%25%

1,1012.5%12.5%

0,0112.5%12.5%

1,0125%0%

0,1112.5%12.5%

1,110%25%1{ } 1{ 0}

1

3{ }

2

1{ }

2

Phase Encoding Principle. Two pulses exit Bob apparatus, and interfere on Alice’s side.

2

2

2

0

2

0

0

0

0

0

2

2

3

2

3

2

Experimental SetupExperimental Setup

Transmitter

Pulse modulator

EncoderLaser ND

filter

Optical fiber

1

Receiver

2(SPD(1

SPD(0(

Encoder

Trigger Card

Synchronizer

DataAcquisition

Bob

Alice

.Serial com

.P.C

.P.C

-0.250.000.25

-0.250.00

0.25

-0.25 0.000.25

-0.25 0.000.25

-0.2

50.

000.

25-0

.25

0.00

0.25

-0.25 0.00 0.25 -0.25 0.00 0.25 -0.25 0.00 0.25 -0.25 0.00 0.25

Single photon Single photon detector (~25% detector (~25%

efficiency )efficiency )

2X2 fiber coupler2X2 fiber coupler(Beam splitter)(Beam splitter)

Polarization Polarization controllercontroller

Phase shifterPhase shifter(Piezoelectric (Piezoelectric

mount)mount)

Nanosecond Nanosecond pulse laserpulse laser

Optical line performance Optical line performance

minmax

minmax

II

IIV

Visibility

S-S pulse

L-S + S-L interference pulse

L-L pulse

Classical regime

Quantum regime

Low Fidelity SourceLow Fidelity Source

Michelson interferometer measurement with short pulses: (a) without interference; (b) & (c) interference with two different phase shifts

Let’s Go To The Q.O. LabLet’s Go To The Q.O. LabFor a DemonstrationFor a Demonstration

The system's Stability - The system's Stability - ~0.3s ~0.3s

Photon lossesPhoton losses – path transmissivity – path transmissivity

Security DiscussionSecurity Discussion

BobBob’s Cheating:’s Cheating:

1.1. Look for correlations between detection efficiency and Look for correlations between detection efficiency and sent qubit base.sent qubit base.

2.2. Alice has different setting time for different measurement Alice has different setting time for different measurement base.base.

3.3. Trojan Horse Attack Trojan Horse Attack

AliceAlice’s Cheating:’s Cheating:

1.1. Non Demolition and Quantum Memory AttackNon Demolition and Quantum Memory Attack('no go theorem' ); not feasible with today's technological limit.('no go theorem' ); not feasible with today's technological limit.

2.2. Random Base AttackRandom Base AttackImposes 25% quantum bit error rate (QBER)Imposes 25% quantum bit error rate (QBER)

3.3. Photon Number Split AttackPhoton Number Split AttackTo prevent this kind of attack the ratio of the probability To prevent this kind of attack the ratio of the probability

for having two photon (or more) in a pulse and Alice'sfor having two photon (or more) in a pulse and Alice's

supposed detection probability must be smaller than one.supposed detection probability must be smaller than one.

4.4. Combined AttackCombined AttackImposes Imposes

( )

1100%

4QBER

Security Discussion with Low Security Discussion with Low Fidelity sourceFidelity source

BobBob has a low fidelity output which imposes an additional has a low fidelity output which imposes an additional QBER (QBER ( ) )

1.1. Random Base Attack:Random Base Attack:ImposesImposes

3.3. Photon Number Split Attack:Photon Number Split Attack:Will not effect PNS like attack Will not effect PNS like attack

4.4. Combined Attack:Combined Attack:Imposes Imposes

B

50%

2BQBER

1 1100%

4 2 BQBER

Final ResultsFinal Results

Opening stage results (1 photon per pulse Opening stage results (1 photon per pulse ) )

•Each protocol took about two hours to be complete

•All QBC protocol results do not exceed the standard deviation range

and are acceptable commitments.

1

Final ResultsFinal Results

•Each protocol took about a day to be complete.

•All QBC protocol results do not exceed the standard deviation range

and are acceptable commitments.

Probably the first practically Probably the first practically secure QBC system in the secure QBC system in the

worldworld

Opening stage results(0.2 photon per Opening stage results(0.2 photon per pulse ) pulse )

Fragile Security- to increase security the number of sent qubits perFragile Security- to increase security the number of sent qubits per

commitment must be increased (2000)commitment must be increased (2000)

1

Future ProspectsFuture Prospects

Improve Quantum Bit Error RateImprove Quantum Bit Error Rate1.1. Single photon source Single photon source

(Spontaneous parametric Down-Conversion)(Spontaneous parametric Down-Conversion)

2.2. Improve pulse coherence Improve pulse coherence

FasterFaster1.1. Real time Labview \ Design DSP circuitsReal time Labview \ Design DSP circuits2.2. Change Piezo with Crystal for E-O modulation (LiNbO3) Change Piezo with Crystal for E-O modulation (LiNbO3)

What did he say?

You You don’t don’t saysay!!

Q&AQ&A