Numerical finite-key analysis of quantum key distribution

Abstract Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable k...

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Autores principales:	Darius Bunandar, Luke C. G. Govia, Hari Krovi, Dirk Englund
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2020
Materias:	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/a41e6c0a09584004aa3c2559bb104c77
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spelling	oai:doaj.org-article:a41e6c0a09584004aa3c2559bb104c772021-12-02T13:58:11ZNumerical finite-key analysis of quantum key distribution10.1038/s41534-020-00322-w2056-6387https://doaj.org/article/a41e6c0a09584004aa3c2559bb104c772020-12-01T00:00:00Zhttps://doi.org/10.1038/s41534-020-00322-whttps://doaj.org/toc/2056-6387Abstract Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.Darius BunandarLuke C. G. GoviaHari KroviDirk EnglundNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 6, Iss 1, Pp 1-12 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
spellingShingle	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Darius Bunandar Luke C. G. Govia Hari Krovi Dirk Englund Numerical finite-key analysis of quantum key distribution
description	Abstract Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.
format	article
author	Darius Bunandar Luke C. G. Govia Hari Krovi Dirk Englund
author_facet	Darius Bunandar Luke C. G. Govia Hari Krovi Dirk Englund
author_sort	Darius Bunandar
title	Numerical finite-key analysis of quantum key distribution
title_short	Numerical finite-key analysis of quantum key distribution
title_full	Numerical finite-key analysis of quantum key distribution
title_fullStr	Numerical finite-key analysis of quantum key distribution
title_full_unstemmed	Numerical finite-key analysis of quantum key distribution
title_sort	numerical finite-key analysis of quantum key distribution
publisher	Nature Portfolio
publishDate	2020
url	https://doaj.org/article/a41e6c0a09584004aa3c2559bb104c77
work_keys_str_mv	AT dariusbunandar numericalfinitekeyanalysisofquantumkeydistribution AT lukecggovia numericalfinitekeyanalysisofquantumkeydistribution AT harikrovi numericalfinitekeyanalysisofquantumkeydistribution AT dirkenglund numericalfinitekeyanalysisofquantumkeydistribution
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Numerical finite-key analysis of quantum key distribution

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