Detection-efficiency mismatch is a common problem in practical quantum key distribution (QKD) systems. Current security proofs of QKD with detection-efficiency mismatch rely either on the assumption of the single-photon light source on the sender side or on the assumption of the single-photon input of the receiver side. These assumptions impose restrictions on the class of possible eavesdropping strategies. Here we present a rigorous security proof without these assumptions and, thus, solve this important problem and prove the security of QKD with detection-efficiency mismatch against general attacks (in the asymptotic regime). In particular, we adapt the decoy state method to the case of detection-efficiency mismatch.
However, security proofs which take into account certain imperfection of hardware devices are still challenging. One of such imperfections is so called detection-efficiency mismatch, where two single-photon detectors have different quantum efficiencies, i.e., different probabilities of photon detection. Such a problem should be taken into account because it is practically impossible to make two absolutely identical detectors.
Mathematically, security proof for QKD with detection-efficiency mismatch for the general case is challenging because the Hilbert space we deal with is infinite-dimensional (a reduction to a finite-dimensional space that is possible for the case of identical detectors does not work here). So, fundamentally new approaches to prove the security was required. The main new method proposed in this work is an analytical bound of the number of multiphoton detection events using the entropic uncertainty relations. This allows us to reduce the problem to a finite-dimensional one. For the analytical solution of the finite-dimensional problem (which is still non-trivial), we propose to use symmetries of the problem.
Thus, in this paper, we proof the security of the BB84 protocol with detection-efficiency mismatch and analytically derive bounds for the secret key rate in this case. Also we adapt the decoy state method to the case of detection-efficiency mismatch.
 C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), p. 175.
 M. Koashi, Simple security proof of quantum key distribution based on complementarity, New J. Phys. 11, 045018 (2009).
 N. Jain, B. Stiller, I. Khan, D. Elser, C. Marquardt, and G. Leuchs, Attacks on practical quantum key distribution systems (and how to prevent them), Contemporary Physics 57, 366 (2015).
 C. H. F. Fung, K. Tamaki, B. Qi, H.-K. Lo, and X. Ma, Security proof of quantum key distribution with detection efficiency mismatch, Quant. Inf. Comput. 9, 131 (2009).
 L. Lydersen and J. Skaar, Security of quantum key distribution with bit and basis dependent detector flaws, Quant. Inf. Comput. 10, 60 (2010).
 M. K. Bochkov and A. S. Trushechkin, Security of quantum key distribution with detection-efficiency mismatch in the single-photon case: Tight bounds, Phys. Rev. A 99, 032308 (2019).
 N. J. Beaudry, T. Moroder, and N. Lütkenhaus, Squashing models for optical measurements in quantum communication, Phys. Rev. Lett. 101, 093601 (2008).
 O. Gittsovich, N. J. Beaudry, V. Narasimhachar, R. R. Alvarez, T. Moroder, and N. Lütkenhaus, Squashing model for detectors and applications to quantum-key-distribution protocols, Phys. Rev. A 89, 012325 (2014).
 Y. Zhang, P. J. Coles, A. Winick, J. Lin, and N. Lütkenhaus, Security proof of practical quantum key distribution with detection-efficiency mismatch, Phys. Rev. Res. 3, 013076 (2021).
 M. Dušek, M. Jahma, and N. Lütkenhaus, Unambiguous state discrimination in quantum cryptography with weak coherent states, Phys. Rev. A 62, 022306 (2000).
 N. Lütkenhaus and M. Jahma, Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack, New J. Phys. 4, 44 (2002).
 Z. Zhang, Q. Zhao, M. Razavi, and X. Ma, Improved key-rate bounds for practical decoy-state quantum-key-distribution systems, Phys. Rev. A 95, 012333 (2017).
 A. S. Trushechkin, E. O. Kiktenko, and A. K. Fedorov, Practical issues in decoy-state quantum key distribution based on the central limit theorem, Phys. Rev. A 96, 022316 (2017).
 C. Agnesi, M. Avesani, L. Calderaro, A. Stanco, G. Foletto, M. Zahidy, A. Scriminich, F. Vedovato, G. Vallone, and P. Villoresi, Simple quantum key distribution with qubit-based synchronization and a self-compensating polarization encoder, Optica 8, 284–290 (2020).
 A. S. Holevo, Quantum Systems, Channels, Information. A Mathematical Introduction (De Gruyter, Berlin, 2012).
 M. Curty, M. Lewenstein, and N. Lütkenhaus, Entanglement as a precondition for secure quantum key distribution, Phys. Rev. Lett. 92, 217903 (2004).
 A. Ferenczi and N. Lütkenhaus, Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning, Phys. Rev. A 85, 052310 (2012).
 E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, Symmetric blind information reconciliation for quantum key distribution, Phys. Rev. Applied 8, 044017 (2017).
 E. O. Kiktenko, A. S. Trushechkin, and A. K. Fedorov, Symmetric blind information reconciliation and hash-function-based verification for quantum key distribution, Lobachevskii J. Math. 39, 992 (2018).
 E. O. Kiktenko, A. O. Malyshev, A. A. Bozhedarov, N. O. Pozhar, M. N. Anufriev, and A. K. Fedorov, Error estimation at the information reconciliation stage of quantum key distribution, J. Russ. Laser Res. 39, 558 (2018).
 D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, Security of quantum key distribution with imperfect devices, Quant. Inf. Comput. 5, 325 (2004).
 P. J. Coles, L. Yu, V Gheorghiu, and R. B. Griffiths, Information-theoretic treatment of tripartite systems and quantum channels, Phys. Rev. A 83, 062338 (2011).
 Y. Zhao, C. H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems, Phys. Rev. A 78, 042333 (2008).
 S. Sajeed, P. Chaiwongkhot, J.-P. Bourgoin, T. Jennewein, N. Lütkenhaus, and V. Makarov, Security loophole in free-space quantum key distribution due to spatial-mode detector-efficiency mismatch, Phys. Rev. A 91, 062301 (2015).
 S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, Advances in quantum cryptography, Adv. Opt. Photon. 12, 1012 (2020).
 M. Bozzio, A. Cavaillés, E. Diamanti, A. Kent, and D. Pitalúa-García, Multiphoton and side-channel attacks in mistrustful quantum cryptography, PRX Quantum 2, 030338 (2021).
 Sukhpal Singh Gill, Adarsh Kumar, Harvinder Singh, Manmeet Singh, Kamalpreet Kaur, Muhammad Usman, and Rajkumar Buyya, "Quantum Computing: A Taxonomy, Systematic Review and Future Directions", arXiv:2010.15559.
 Mathieu Bozzio, Adrien Cavaillès, Eleni Diamanti, Adrian Kent, and Damián Pitalúa-García, "Multiphoton and Side-Channel Attacks in Mistrustful Quantum Cryptography", PRX Quantum 2 3, 030338 (2021).
 Yanbao Zhang, Patrick J. Coles, Adam Winick, Jie Lin, and Norbert Lütkenhaus, "Security proof of practical quantum key distribution with detection-efficiency mismatch", Physical Review Research 3 1, 013076 (2021).
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