Deterministic Quantum Key Distribution with Untrusted Relay and Finite Sources
Guo-Dong Kang, Li-Jun Zhang, Xiao-Lu Wu, Qing-Ping Zhou, Mao-Fa Fang
pp. 542-551 · 10.2478/qic-2025-0029
On this page
Abstract
Measurement-device-independent quantum key distribution (MDI-QKD) is proposed to close all loopholes of detection devices in QKD systems, and it holds the potential to double the limit transmission distance of those one-way QKD protocols. However, most MDI-QKD protocols are nondeterministic, which reduces the potential key rate by nearly half. In this paper, we propose a deterministic QKD protocol with an untrusted detection relay and finite sources, and based on the current technology of QKD devices, we derive the performance formula for it. The simulation results show that the performance of this protocol can exceed the MDI-QKD within the long limit transmission distance range, about 445km.
Open accessCC BY-NC-ND 4.0
Keywords
- Deterministic Quantum Key Distribution
- Untrusted Relay
- Finite Sources
Suggested citation
Guo-Dong Kang, Li-Jun Zhang, Xiao-Lu Wu, Qing-Ping Zhou, Mao-Fa Fang (2025). Deterministic Quantum Key Distribution with Untrusted Relay and Finite Sources. Quantum Information & Computation, 25(5), 542-551. https://doi.org/10.2478/qic-2025-0029
References (35)
- C. H. Bennett, and G. Brassard (1984). “Quantum cryptography: Public key distribution and coin tossing”. Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, 175–179.Google Scholar
- A. K. Ekert (1991). “Quantum cryptography based on Bell’s theorem”. Physical Review Letters, 67: 6, 661–663.DOI: 10.1103/PhysRevLett.67.661Google Scholar
- H.-K. Lo, and H. Chau (1999). “Unconditional security of quantum key distribution over arbitrarily long distances”. Science, 283: 5410, 2050–2056.DOI: 10.1126/science.283.5410.2050Google Scholar
- D. Mayers (1996). “Quantum key distribution and string oblivious transfer in noisy channels”. Advances in Cryptology—CRYPTO’96, 343–357. Heidelberg: Springer.DOI: 10.1007/3-540-68697-5_26Google Scholar
- P. W. Shor, and J. Preskill (2000). “Simple proof of security of the BB84 quantum key distribution protocol”. Physical Review Letter, 85: 2, 441–444.DOI: 10.1103/PhysRevLett.85.441Google Scholar
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden (2002). “Quantum cryptography”. Reviews of Modern Physics, 74: 1, 145–200.DOI: 10.1103/RevModPhys.74.145Google Scholar
- C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin (1992). “Experimental quantum cryptography”. Journal. of Cryptology, 5, 3–28.DOI: 10.1007/BF00191318Google Scholar
- S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, C.-W. Liao, H.-F. Zhang, Y.-J. Han, W.-Y. Zhou, H.-S. Zhong, H.-Z. Lu, Z.-Z. Zhang, X.-L. Chen, J.-Z. Zhang, F.-X. Li, Z.-S. Yuan, and J.-W. Pan (2017). “Satellite-to-ground quantum key distribution”. Nature, 549: 43–47, 2017.DOI: 10.1038/nature23655Google Scholar
- H. K. Lo, X. Ma, and K. Chen (2005). “Decoy state quantum key distribution”. Physical Review Letter, 94, 230504.DOI: 10.1103/PhysRevLett.94.230504Google Scholar
- X. B. Wang (2005). “Beating the photon-number-splitting attack in practical quantum cryptography”. Physical Review Letter, 94, 230503.DOI: 10.1103/PhysRevLett.94.230503Google Scholar
- H. K. Lo, M. Curty, and B. Qi (2012). “Measurement-device-independent quantum key distribution”. Physical Review Letter, 108, 130503.DOI: 10.1103/PhysRevLett.108.130503Google Scholar
- Z.-Q. Yin, C.-H. Fred Fung, X. Ma, C.-M. Zhang, H.-W. Li, Wei Chen, S. Wang, G.-C. Guo, and Z.-F. Han (2013). “Measurement-device-independent quantum key distribution with uncharacterized qubit sources”. Physical Review A, 88: 6, 1–9.DOI: 10.1103/PhysRevA.88.062322Google Scholar
- G.-D. Kang, Q.-P. Zhou, and M.-F. Fang (2019). “Measurement-device-independent quantum key distribution with uncharacterized coherent sources”. Quantum Information Processing, 19: 1, 1–18.DOI: 10.1007/s11128-019-2494-0Google Scholar
- K. Boström and T. Felbinger (2002). “Deterministic secure direct communication using entanglement”. Physical Review Letter, 89: 1, 187902.DOI: 10.1103/PhysRevLett.89.187902Google Scholar
- M. Lucamarini, and S. Mancini (2005). “Secure deterministic communication without entanglement”. Physical Review Letter,94: 14, 140501.DOI: 10.1103/PhysRevLett.94.140501Google Scholar
- H. Lu, C.-H. Fred Fung, X.-F. Ma, and Q.-Y. Cai (2011). “Unconditional security proof of a deterministic quantum key distribution with a two-way quantum channel”. Physical Review. A, 84: 4, 1504–1512.DOI: 10.1103/PhysRevA.84.042344Google Scholar
- N. J. Beaudry, M. Lucamarini, S. Mancini, and R. Renner (2013). “Security of two-way quantum key distribution”. Physical Review A, 88: 6, 8617–8626.DOI: 10.1103/PhysRevA.88.062302Google Scholar
- C.-H. Fred Fung, X. Ma, H. Chau, and Q.-Y. Cai (2012). “Quantum key distribution with delayed privacy amplification and its application to the security proof of a two-way deterministic protocol”. Physical Review A, 85: 3, 032308.DOI: 10.1103/PhysRevA.85.032308Google Scholar
- G.-D. Kang, Q.-P. Zhou, and M.-F. Fang (2019). “Two-way quantum key distribution in a uniformly distributed quantum space via a special mapping and its analytical security proofs”. International Journal of Quantum Information, 17: 1, 19500102.DOI: 10.1142/S0219749919500102Google Scholar
- M. Lucamarini, A. Cere’, G. D. Giuseppe, S. Mancini, D. Vitali, and P Tombesi (2007). “Two-way protocol for quantum cryptography with imperfect devices”. Open System and Information Dynamics, 14, 169–178.DOI: 10.1007/s11080-007-9045-3Google Scholar
- L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov. (2010). “Hacking commercial quantum cryptography systems by tailored bright illumination”. Nature Photonics, 4: 10, 686–689.DOI: 10.1038/nphoton.2010.214Google Scholar
- H. Lu, C.-H. F. Fung, and Q.-Y. Cai (2013). “Two-way deterministic quantum key distribution against detectorside-channel attacks”. Physical Review A, 88: 4, 044302.DOI: 10.1103/PhysRevA.88.044302Google Scholar
- Y. Ma, Y.-Z. Ma, Z.-Q. Zhou, C.-F. Li, and G.-C. Guo (2021). “One-hour coherent optical storage in an atomic frequency comb memory”. Nature Communications, 12: 1, 2381.DOI: 10.1038/s41467-021-22706-yGoogle Scholar
- Q.-Y. Cai (2003). “The ping-pong protocol can be attacked without eavesdropping”. Physical Review Letter, 91, 109801.DOI: 10.1103/PhysRevLett.91.109801Google Scholar
- A. Wójcik (2003). “Eavesdropping on the “ping-pong” quantum communication protocol”. Physical Review Letter, 90: 15: 157901.DOI: 10.1103/PhysRevLett.90.157901Google Scholar
- R. Koenig, U. Maurer, and R. Renner (2022). “On the power of quantum memory”. IEEE Transactions Information Theory, 51, 2391–2401.DOI: 10.1109/TIT.2005.850087Google Scholar
- H.-Z. J. Zeng, M. A. P. Nguyen, X. Ai, A. Bennett, A. S. Solntsev, A. Laucht, M. T. L. S. L. Tang, and P. K. Lam, (2022). “Integrated room temperature single-photon source for quantum key distribution”. Optics Letters, 47: 7, 1673–1676.DOI: 10.1364/OL.454450Google Scholar
- X.-F. Ma, B. Qi, Y. Zhao, and H.-K. Lo (2025). “Practical decoy state for quantum key distribution”. Physical Review A,72: 1,012326.Google Scholar
- A. El Gamal and Y. H. Kim (2011). Network Information Theory, Cambridge: Cambridge University Press.DOI: 10.1017/CBO9781139030687Google Scholar
- H.-W. Li, Y.-B. Zhao, Z.-Q. Yin, S. Wang, Z.-F. Han, W-S. Bao, and G.-C. Guo (2009). “Security of decoy states QKD with finite resources against collective attacks”. Optics Communications, 282: 20, 4162–4166.DOI: 10.1016/j.optcom.2009.07.011Google Scholar
- M. Christandl, R. Koenig, and R. Renner (2008). “Post-selection technique for quantum channels with applications to quantum cryptography”. Physical Review Letter, 102: 2, 020504.DOI: 10.1103/PhysRevLett.102.020504Google Scholar
- X.-F. Ma, P. Zeng and H.-Y. Zhou (2018). “Phase-matching quantum key distribution”. Physical Review X,8: 3, 0310431.DOI: 10.1103/PhysRevX.8.031043Google Scholar
- L. Zhou, J.-P. Lin, Y.-M. Xie, Y.-S. Lu, Y.-M. Jing, H.-L. Yin and Z.-L. Yuan (2023). “Experimental quantum communication overcomes the rate-loss limit without global phase tracking”. Physical Review Letters, 130, 250801.DOI: 10.1103/PhysRevLett.130.250801Google Scholar
- Z.-R. Zhou, Y.-B. Sheng, P.-H. Niu, L.-G. Yin, G.-L. Long, and L. Hanzo (2019). “Measurement-device-independent quantum secure direct communication”. Science China Physics, Mechanics & Astronomy, 63: 3, 230362.DOI: 10.1007/s11433-019-1450-8Google Scholar
- R. Jozsa, and J. Schlienz (1999). “Distinguishability of states and von Neumann entropy”. Physical Review A, 62, 012301.DOI: 10.1103/PhysRevA.62.012301Google Scholar
