Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture
A long-standing open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2012
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| Online Access: | http://hdl.handle.net/1721.1/71640 https://orcid.org/0000-0002-6094-5861 |
| _version_ | 1811073303161339904 |
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| author | Garcia-Patron Sanchez, Raul Navarrete-Benlloch, Carlos Lloyd, Seth Shapiro, Jeffrey H. Cerf, Nicolas J. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Garcia-Patron Sanchez, Raul Navarrete-Benlloch, Carlos Lloyd, Seth Shapiro, Jeffrey H. Cerf, Nicolas J. |
| author_sort | Garcia-Patron Sanchez, Raul |
| collection | MIT |
| description | A long-standing open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory. |
| first_indexed | 2024-09-23T09:31:00Z |
| format | Article |
| id | mit-1721.1/71640 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:31:00Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/716402022-09-26T11:57:00Z Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture Garcia-Patron Sanchez, Raul Navarrete-Benlloch, Carlos Lloyd, Seth Shapiro, Jeffrey H. Cerf, Nicolas J. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Research Laboratory of Electronics Shapiro, Jeffrey H. Garcia-Patron Sanchez, Raul Navarrete-Benlloch, Carlos Lloyd, Seth Shapiro, Jeffrey H. Cerf, Nicolas J. A long-standing open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory. Alexander von Humboldt-Stiftung Belgian National Foundation for Scientific Research European Union (Project No. FIS2008-06024-C03-01) W. M. Keck Foundation Center for Extreme Quantum Information Theory Spain. Ministerio de Ciencia e Innovación (MICINN) (FPU) United States. Office of Naval Research (Basic Research Challenge Program) Fondation pour la recherche strategique (France) (HIPERCOM) 2012-07-17T12:43:02Z 2012-07-17T12:43:02Z 2012-03 2011-11 Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/71640 García-Patrón, Raúl et al. “Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture.” Physical Review Letters 108.11 (2012). © 2012 American Physical Society https://orcid.org/0000-0002-6094-5861 en_US http://dx.doi.org/10.1103/PhysRevLett.108.110505 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Garcia-Patron Sanchez, Raul Navarrete-Benlloch, Carlos Lloyd, Seth Shapiro, Jeffrey H. Cerf, Nicolas J. Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture |
| title | Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture |
| title_full | Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture |
| title_fullStr | Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture |
| title_full_unstemmed | Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture |
| title_short | Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture |
| title_sort | majorization theory approach to the gaussian channel minimum entropy conjecture |
| url | http://hdl.handle.net/1721.1/71640 https://orcid.org/0000-0002-6094-5861 |
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