80
5 Quantum Key Distribution with Imperfect Devices
the MDI-QKD protocol are those where both Alice and Bob sent a single photon to
the relay. Moreover, a detection event is successful only when exactly two detectors
clicked in the combinations described above.
The authors in [13] provide the asymptotic secret key rate achieved by their MDIQKD protocol. They consider a version of the protocol where the rectilinear basis is
used for key generation and the diagonal basis (selected in a small fraction of rounds)
is used for estimating Eve’s knowledge (PE). The resulting secret key rate reads:
r MDI = Q
1,1
rect (1 − h(e
1,1
diag )) − Q rect h(E rect ),
(5.19)
where Q rect and E rect are the gain and QBER of the signal state in the rectilinear
basis. That is, Q rect is the probability of a successful detection given that both Alice
and Bob sent a signal state in the rectilinear basis. Instead, Q
1,1
rect is the probability
that both parties sent one photon and the relay had a successful detection, given that
they both prepared a signal state in the rectilinear basis. Finally e
1,1
diag is the error rate
in the diagonal basis given that Alice and Bob sent one photon each and the detection
was successful.
As expected, the secret key rate in (5.19) resembles the one in (5.12) of an asymmetric BB84 protocol with decoy states. Similarly to that case, the quantities Q
1,1
rect
and e
1,1
diag can be bounded with the decoy state method presented in the previous
Section.
References
1. Huttner, B., Imoto, N., Gisin, N., & Mor, T. (1995). Quantum cryptography with coherent
states. Physical Review A, 51, 1863–1869.
2. Brassard, G., Lütkenhaus, N., Mor, T., & Sanders, B. C. (2000). Limitations on practical
quantum cryptography. Physical Review Letters, 85, 1330–1333.
3. Gottesman, D., Lo, H.-K., Lütkenhaus, N., & Preskill, J. (2004). Security of quantum key
distribution with imperfect devices. Quantum Information & Computation, 4, 325–360.
4. Lo, H.-K., Ma, X., & Chen, K. (2005). Decoy state quantum key distribution. Physical Review
Letters, 94, 230504.
5. Wei, Z., Wang, W., Zhang, Z., Gao, M., Ma, Z., & Ma, X. (2013). Decoy-state quantum key
distribution with biased basis choice. Scientific Reports, 3(1), 2453.
6. Hwang, W.-Y. (2003). Quantum key distribution with high loss: Toward global secure communication. Physical Review Letters, 91, 057901.
7. Wang, X.-B. (2005). Beating the photon-number-splitting attack in practical quantum cryptography. Physical Review Letters, 94, 230503.
8. Lim, C. C. W., Curty, M., Walenta, N., Xu, F., & Zbinden, H. (2014). Concise security bounds
for practical decoy-state quantum key distribution. Physical Review A, 89, 022307.
9. Rusca, D., Boaron, A., Grünenfelder, F., Martin, A., & Zbinden, H. (2018). Finite-key analysis
for the 1-decoy state qkd protocol. Applied Physics Letters, 112(17), 171104.
10. Zhao, Y., Fung, C.-H. F., Qi, B., Chen, C., & Lo, H.-K. (2008). Quantum hacking: Experimental
demonstration of time-shift attack against practical quantum-key-distribution systems. Physical
Review A, 78, 042333.
5 Quantum Key Distribution with Imperfect Devices
the MDI-QKD protocol are those where both Alice and Bob sent a single photon to
the relay. Moreover, a detection event is successful only when exactly two detectors
clicked in the combinations described above.
The authors in [13] provide the asymptotic secret key rate achieved by their MDIQKD protocol. They consider a version of the protocol where the rectilinear basis is
used for key generation and the diagonal basis (selected in a small fraction of rounds)
is used for estimating Eve’s knowledge (PE). The resulting secret key rate reads:
r MDI = Q
1,1
rect (1 − h(e
1,1
diag )) − Q rect h(E rect ),
(5.19)
where Q rect and E rect are the gain and QBER of the signal state in the rectilinear
basis. That is, Q rect is the probability of a successful detection given that both Alice
and Bob sent a signal state in the rectilinear basis. Instead, Q
1,1
rect is the probability
that both parties sent one photon and the relay had a successful detection, given that
they both prepared a signal state in the rectilinear basis. Finally e
1,1
diag is the error rate
in the diagonal basis given that Alice and Bob sent one photon each and the detection
was successful.
As expected, the secret key rate in (5.19) resembles the one in (5.12) of an asymmetric BB84 protocol with decoy states. Similarly to that case, the quantities Q
1,1
rect
and e
1,1
diag can be bounded with the decoy state method presented in the previous
Section.
References
1. Huttner, B., Imoto, N., Gisin, N., & Mor, T. (1995). Quantum cryptography with coherent
states. Physical Review A, 51, 1863–1869.
2. Brassard, G., Lütkenhaus, N., Mor, T., & Sanders, B. C. (2000). Limitations on practical
quantum cryptography. Physical Review Letters, 85, 1330–1333.
3. Gottesman, D., Lo, H.-K., Lütkenhaus, N., & Preskill, J. (2004). Security of quantum key
distribution with imperfect devices. Quantum Information & Computation, 4, 325–360.
4. Lo, H.-K., Ma, X., & Chen, K. (2005). Decoy state quantum key distribution. Physical Review
Letters, 94, 230504.
5. Wei, Z., Wang, W., Zhang, Z., Gao, M., Ma, Z., & Ma, X. (2013). Decoy-state quantum key
distribution with biased basis choice. Scientific Reports, 3(1), 2453.
6. Hwang, W.-Y. (2003). Quantum key distribution with high loss: Toward global secure communication. Physical Review Letters, 91, 057901.
7. Wang, X.-B. (2005). Beating the photon-number-splitting attack in practical quantum cryptography. Physical Review Letters, 94, 230503.
8. Lim, C. C. W., Curty, M., Walenta, N., Xu, F., & Zbinden, H. (2014). Concise security bounds
for practical decoy-state quantum key distribution. Physical Review A, 89, 022307.
9. Rusca, D., Boaron, A., Grünenfelder, F., Martin, A., & Zbinden, H. (2018). Finite-key analysis
for the 1-decoy state qkd protocol. Applied Physics Letters, 112(17), 171104.
10. Zhao, Y., Fung, C.-H. F., Qi, B., Chen, C., & Lo, H.-K. (2008). Quantum hacking: Experimental
demonstration of time-shift attack against practical quantum-key-distribution systems. Physical
Review A, 78, 042333.