Majorisation‐minimisation algorithm for optimal state discrimination in quantum communications
Abstract Designing optimal measurement operators for quantum state discrimination (QSD) is an important problem in quantum communications and cryptography applications. Prior works have demonstrated that optimal quantum measurement operators can be obtained by solving a convex semidefinite program (...
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| Format: | Article |
| Language: | English |
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Wiley
2024-12-01
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| Series: | IET Quantum Communication |
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| Online Access: | https://doi.org/10.1049/qtc2.12107 |
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| author | Neel Kanth Kundu Prabhu Babu Petre Stoica |
| author_facet | Neel Kanth Kundu Prabhu Babu Petre Stoica |
| author_sort | Neel Kanth Kundu |
| collection | DOAJ |
| description | Abstract Designing optimal measurement operators for quantum state discrimination (QSD) is an important problem in quantum communications and cryptography applications. Prior works have demonstrated that optimal quantum measurement operators can be obtained by solving a convex semidefinite program (SDP). However, solving the SDP can represent a high computational burden for many real‐time quantum communication systems. To address this issue, a majorisation‐minimisation (MM)‐based algorithm, called Quantum Majorisation‐Minimisation (QMM) is proposed for solving the QSD problem. In QMM, the authors reparametrise the original objective, then tightly upper‐bound it at any given iterate, and obtain the next iterate as a closed‐form solution to the upper‐bound minimisation problem. Our numerical simulations demonstrate that the proposed QMM algorithm significantly outperforms the state‐of‐the‐art SDP algorithm in terms of speed, while maintaining comparable performance for solving QSD problems in quantum communication applications. |
| format | Article |
| id | doaj-art-dd3bde8edfa0467c9031c9411a1aefe3 |
| institution | DOAJ |
| issn | 2632-8925 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Quantum Communication |
| spelling | doaj-art-dd3bde8edfa0467c9031c9411a1aefe32025-08-20T02:39:38ZengWileyIET Quantum Communication2632-89252024-12-015461261810.1049/qtc2.12107Majorisation‐minimisation algorithm for optimal state discrimination in quantum communicationsNeel Kanth Kundu0Prabhu Babu1Petre Stoica2Centre for Applied Research in Electronics (CARE) Indian Institute of Technology Delhi New Delhi IndiaCentre for Applied Research in Electronics (CARE) Indian Institute of Technology Delhi New Delhi IndiaDivision of Systems and Control, Department of Information Technology Uppsala University Uppsala SwedenAbstract Designing optimal measurement operators for quantum state discrimination (QSD) is an important problem in quantum communications and cryptography applications. Prior works have demonstrated that optimal quantum measurement operators can be obtained by solving a convex semidefinite program (SDP). However, solving the SDP can represent a high computational burden for many real‐time quantum communication systems. To address this issue, a majorisation‐minimisation (MM)‐based algorithm, called Quantum Majorisation‐Minimisation (QMM) is proposed for solving the QSD problem. In QMM, the authors reparametrise the original objective, then tightly upper‐bound it at any given iterate, and obtain the next iterate as a closed‐form solution to the upper‐bound minimisation problem. Our numerical simulations demonstrate that the proposed QMM algorithm significantly outperforms the state‐of‐the‐art SDP algorithm in terms of speed, while maintaining comparable performance for solving QSD problems in quantum communication applications.https://doi.org/10.1049/qtc2.12107computational complexityHilbert spacesmatrix algebraquantum communicationquantum informationquantum optics |
| spellingShingle | Neel Kanth Kundu Prabhu Babu Petre Stoica Majorisation‐minimisation algorithm for optimal state discrimination in quantum communications IET Quantum Communication computational complexity Hilbert spaces matrix algebra quantum communication quantum information quantum optics |
| title | Majorisation‐minimisation algorithm for optimal state discrimination in quantum communications |
| title_full | Majorisation‐minimisation algorithm for optimal state discrimination in quantum communications |
| title_fullStr | Majorisation‐minimisation algorithm for optimal state discrimination in quantum communications |
| title_full_unstemmed | Majorisation‐minimisation algorithm for optimal state discrimination in quantum communications |
| title_short | Majorisation‐minimisation algorithm for optimal state discrimination in quantum communications |
| title_sort | majorisation minimisation algorithm for optimal state discrimination in quantum communications |
| topic | computational complexity Hilbert spaces matrix algebra quantum communication quantum information quantum optics |
| url | https://doi.org/10.1049/qtc2.12107 |
| work_keys_str_mv | AT neelkanthkundu majorisationminimisationalgorithmforoptimalstatediscriminationinquantumcommunications AT prabhubabu majorisationminimisationalgorithmforoptimalstatediscriminationinquantumcommunications AT petrestoica majorisationminimisationalgorithmforoptimalstatediscriminationinquantumcommunications |