Development of decoy-state quantum key distribution

Xiang-Bin Wang

BB84 protocol：k𝐞𝐲 𝐫𝐚𝐭𝐞 𝐑~𝐎(𝜼)

One-time pad

Quantum indivisibility

Quantum non-cloning theorem

Eavesdropper will be found

Encrypted content cannot be deciphered

• Channel Loss

• Eve’s channel

Alice

E

V

E Bob

B. Huttner et al, Phys. Rev. A51, 1863(1985)

G. Brassard et al, Phys. Rev. Lett., 85, 1330(2000)

Secure distance is less than 20 km ！

Imperfect sources might be attacked by PNS

( ) ( ) ( )1 11

HR HH H

= − − − − −

− −

The fraction of multi-photons

Bit-flip error rate

The fraction of single-photons

( ) ( ) ( )2 2log 1 log 1H x x x x x= − − − −

Estimate the lower bound of

H. Inamori, N. Lutkenhaus and D. Mayers, quant-ph/0107017;

D. Gottesman et al, Quantum. Inf. Comput., 4, 325(2004)

Formula for the secure key rate——ILM-GLLP formula

𝑛0𝑛𝜇𝑛𝜇′

Y.Y. Hwang, PRL, 2003

X.-B. Wang, quant-ph/0410075,

Phys. Rev. Lett. 94, 230503(2005)

H.K. Lo et al, PRL, 2005

Decoy state method

X.-B. Wang et al, Physics Reports, 2007

Alice BobEve

0

𝜇𝜇′

The main idea is to change the source randomly

𝑆𝜌 = 𝑆𝜌′

𝑠1 = 𝑠1′

Encoding: four BB84 states

0

𝝁𝒙

𝝁𝒚

Intensity choice

Vacuum source

Signal source y

Decoy source x

basis

bitX-basis Z-basis

𝟎

𝟏

Decoy-state method MDIQKD protocol：key rate 𝐑~𝐎(𝜼)

X.-B. Wang, Phys. Rev. A 87, 012320 (2013)

S.L. Braunstein, PRL 2011

H.K. Lo et al, PRL 2011

Improvement of the MDIQKD protocol

Joint constraints for statistical fluctuations：Phys. Rev. A 91, 032318 (2015).

Four-intensity protocol：Phys. Rev. A 93, 042324 (2016).

Improve the key rate greatly!

1) 404 km, low-loss fiber

2) 311 km, normal fiber

3) Key rate at 207 km increased

by more than 500 times

4) Exceed the limit distance of

BB84 protocol

Twin-Field (TF) QKD protocol：overcome the linear bound

The advantage of TFQKD: improving the key rate from R~𝑂(𝜂) to R~𝑂( 𝜂).

M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J.Shields, Nature 557, 400 (2018).

Alice and Bob send the states ±𝜇 , ±𝑖𝜇 randomly.

The signal state is the two-mode single-photon state 01 ± 10

2

——𝑅~𝑂( 𝜂)

M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J.Shields, Nature 557, 400 (2018).

Twin-Field (TF) QKD protocol：overcome the linear bound

Modified protocols based on TF-QKD

➢ Sending or not-sending (SNS) QKD protocol：X.-B. Wang, Z.-W. Yu, X.-L. Hu, Phys. Rev.

A 98, 062323 (2018).

➢ TF* QKD protocol：K. Tamaki, H.-K. Lo, W. Wang, and M. Lucamarini, arXiv preprint

arXiv:1805.05511 (2018).

➢ Phase-Matching QKD protocol ： X. Ma, P. Zeng, and H. Zhou, Physical Review X 8, 031043

(2018).

➢ TFQKD protocol without post-selection of the phase：C. Cui, Z.-Q. Yin, R. Wang, W. Chen, S.

Wang, G.-C. Guo, and Z.-F. Han, Physical Review Applied 11, 034053 (2019)；M. Curty, K.

Azuma, and H.-K. Lo, arXiv preprint arXiv:1807.07667 (2018).

Sending or not sending （SNS）TFQKD protocol

Schematic picture of SNS protocol

Target states:Z-window—— 01 , 10

X-window——( 01 + 10 )/ 2

( 01 − 10 )/ 2

Decoy-state method：Z-window——Alice and Bob each sends a coherentstate 𝛼𝑍 with probability pZ , or sends a vacuumpulse with probability 1-pZ

X-window——Alice and Bob each sends a coherentstate 𝛼𝑖 with probability pi , 𝑖 = 1,2, … , or sends avacuum pulse with probability 1-σ𝑖 𝑝𝑖

X.-B. Wang, Z.-W. Yu, X.-L. Hu, Phys. Rev. A 98, 062323 (2018)

Advantage of SNS protocol：the security under coherent attack has been proved; can tolerate large misalignment error; key rate 𝑅~𝑂( 𝜂).

𝑙 = 𝑛1 1 − ℎ 𝑒1𝑝ℎ

− 𝑓𝑛𝑡ℎ(𝐸𝑍)

SNS-QKD protocol

X.-B. Wang, Z.-W. Yu, X.-L. Hu, Phys. Rev. A 98, 062323 (2018)

1) Encoding by sending or not-sending

a coherent state

2) Secure distance increases by twice.

3) Tolerate misalignment error

4) Compared with MDI, the key rate at

404 km is increased by 5-6 orders of

magnitude.

Experiment of SNS protocol

The proof-of-principle experiment demonstrated by Toshiba Research Europe Ltd, Cambridge [Nature Photonics, 1 (2019)]：

Ref. 24 is SNS protocol

The experiment in fiber in cooperation with the team of the University of Science and Technology of China [arXiv:1902.06268 (2019)]：

Experiment of SNS protocol

Experiments of other kinds of TFQKD

S. Wang, D.-Y. He, Z.-Q. Yin, F.-Y. Lu,

C.-H. Cui, W. Chen, Z. Zhou, G.-C.

Guo, and Z.-F. Han, arXiv:1902.06884

(2019).

TFQKD protocol without post-selection

of the phase

X. Zhong, J. Hu, M. Curty, L. Qian,

and H.-K. Lo, arXiv:1902.10209

(2019).

TF* QKD protocol

Development of the theory of SNS: finite key-size effect

Z.-W. Yu, X.-L. Hu, C. Jiang, H. Xu, and X.-B. Wang,Scientific reports 9, 3080 (2019).

With the finite key-size effect, the key rate of SNS protocol is still higher than PLOB bound.

• Finite number of the decoy sources

• Statistical fluctuation in the estimation of parameters

• Finite size of the phase-slice

𝑙 = 𝑛1 1 − ℎ 𝑒1𝑝ℎ

− 𝑓𝑛𝑡ℎ(𝐸𝑍) − log22

𝜀𝑐𝑜𝑟− 2 log2

1

2 𝜀𝑃𝐴 𝜀

C. Jiang, Z.-W. Yu, X.-L. Hu, and X.-B. Wang, arXiv: 1904.00192 (2019).

A key rate formula containing thefull finite key-size effect isobtained under the composablesecurity framework.

Development of the theory of SNS: finite key-size effect

Development of the theory of SNS: Post processing of error rejection with two-way classical communication

The bit-flip error rate can be reduced by post processing of error rejection with two-way classical communication, hence improving the key rate[arXiv: 1904.06331 (2019) ]:

Eq.(24): Active Odd-Parity PairingEq.(17): Odd-Parity Sifting with Random PairingEq.(9): Random PairingEq.(4): Refined Structure of Bit-flip Error RateRef. (63): Original SNS

Thank you!