

Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2020
November 25, 2020 16:15–16:30, Moscow, online






Security proof for a protocol of quantum key distribution
A. S. Trushechkin^{} 
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Abstract:
Quantum cryptography is a modern branch of science where methods of secure communication based on principles of quantum mechanics are studied. The rigorous proof of the security of quantum cryptography (more precisely, quantum key distribution) gave rise to a complex and beautiful mathematical theory, which is based on methods of quantum information theory, in particular, quantum entropic measures and entropic uncertainty relations. Currently, an important task is to prove the security of quantum key distribution with imperfect devices. In the talk, the results of papers [1, 2] will be reported. In these papers, theorems on the security of the celebrated BB84 quantum key distribution protocol (the first and most widely used protocol) with detectionefficiency mismatch were rigorously proved for the first time. The differences in the detector efficiencies (the probabilities of detecting a photon) destroys certain symmetries in the problem, which makes the earlier methods of security proofs insufficient. In [1, 2], new methods for analytic solution of a minimization problem of a certain convex functional (quantum relative entropy) and methods for bounding the dimensionality of the search space under were developed. This was one of the key problems for solving this problem. In [3], some statements were proved that explain the operational meaning of the security parameter widely used in quantum key distribution.
References

M. K. Bochkov, A. S. Trushechkin, “Security of quantum key distribution with detectionefficiency mismatch in the singlephoton case: Tight bounds”, Phys. Rev. A, 99:3 (2019), 32308, 15 с.

A. S. Trushechkin, Security of quantum key distribution with detectionefficiency mismatch in the multiphoton case, arXiv: 2004.07809

A. S. Trushechkin, “Ob operatsionnom smysle i prakticheskikh aspektakh ispolzovaniya parametra stoikosti v kvantovom raspredelenii klyuchei”, Kvantovaya elektronika, 50:5 (2020), 426–439
^{*} Zoom Meeting ID: 979 5396 3790
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