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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2020-12-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-020-00322-w |
| _version_ | 1818754040860770304 |
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| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-18T05:16:56Z |
| format | Article |
| id | doaj.art-a41e6c0a09584004aa3c2559bb104c77 |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-12-18T05:16:56Z |
| publishDate | 2020-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-a41e6c0a09584004aa3c2559bb104c772022-12-21T21:19:45ZengNature Portfolionpj Quantum Information2056-63872020-12-016111210.1038/s41534-020-00322-wNumerical finite-key analysis of quantum key distributionDarius Bunandar0Luke C. G. Govia1Hari Krovi2Dirk Englund3Research Laboratory of Electronics, Massachusetts Institute of TechnologyRaytheon BBN TechnologiesRaytheon BBN TechnologiesResearch Laboratory of Electronics, Massachusetts Institute of TechnologyAbstract 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.https://doi.org/10.1038/s41534-020-00322-w |
| spellingShingle | Darius Bunandar Luke C. G. Govia Hari Krovi Dirk Englund Numerical finite-key analysis of quantum key distribution npj Quantum Information |
| title | 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_short | Numerical finite-key analysis of quantum key distribution |
| title_sort | numerical finite key analysis of quantum key distribution |
| url | https://doi.org/10.1038/s41534-020-00322-w |
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