Strong subadditivity for log-determinant of covariance matrices and its applications
We prove that the log-determinant of the covariance matrix obeys the strong subadditivity inequality for arbitrary tripartite states of multimode continuous variable quantum systems. This establishes general limitations on the distribution of information encoded in the second moments of canonically...
| Main Authors: | , |
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| Format: | Article |
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IOP
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40789/ |
| _version_ | 1848796133839601664 |
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| author | Adesso, Gerardo Simon, R. |
| author_facet | Adesso, Gerardo Simon, R. |
| author_sort | Adesso, Gerardo |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We prove that the log-determinant of the covariance matrix obeys the strong subadditivity inequality for arbitrary tripartite states of multimode continuous variable quantum systems. This establishes general limitations on the distribution of information encoded in the second moments of canonically conjugate operators. The inequality is shown to be stronger than the conventional strong subadditivity inequality for von Neumann entropy in a class of pure tripartite Gaussian states. We finally show that such an inequality implies a strict monogamy-type constraint for joint Einstein-Podolsky-Rosen steerability of single modes by Gaussian measurements performed on multiple groups of modes. |
| first_indexed | 2025-11-14T19:43:09Z |
| format | Article |
| id | nottingham-40789 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:09Z |
| publishDate | 2016 |
| publisher | IOP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-407892020-05-04T17:59:59Z https://eprints.nottingham.ac.uk/40789/ Strong subadditivity for log-determinant of covariance matrices and its applications Adesso, Gerardo Simon, R. We prove that the log-determinant of the covariance matrix obeys the strong subadditivity inequality for arbitrary tripartite states of multimode continuous variable quantum systems. This establishes general limitations on the distribution of information encoded in the second moments of canonically conjugate operators. The inequality is shown to be stronger than the conventional strong subadditivity inequality for von Neumann entropy in a class of pure tripartite Gaussian states. We finally show that such an inequality implies a strict monogamy-type constraint for joint Einstein-Podolsky-Rosen steerability of single modes by Gaussian measurements performed on multiple groups of modes. IOP 2016-07-22 Article PeerReviewed Adesso, Gerardo and Simon, R. (2016) Strong subadditivity for log-determinant of covariance matrices and its applications. Journal of Physics A: Mathematical and Theoretical, 49 (34). 34LT02. ISSN 1751-8113 http://iopscience.iop.org/article/10.1088/1751-8113/49/34/34LT02/meta;jsessionid=43AE706290A778E5437CC22026CDAA2E.c2.iopscience.cld.iop.org doi:10.1088/1751-8113/49/34/34LT02 doi:10.1088/1751-8113/49/34/34LT02 |
| spellingShingle | Adesso, Gerardo Simon, R. Strong subadditivity for log-determinant of covariance matrices and its applications |
| title | Strong subadditivity for log-determinant of covariance matrices and its applications |
| title_full | Strong subadditivity for log-determinant of covariance matrices and its applications |
| title_fullStr | Strong subadditivity for log-determinant of covariance matrices and its applications |
| title_full_unstemmed | Strong subadditivity for log-determinant of covariance matrices and its applications |
| title_short | Strong subadditivity for log-determinant of covariance matrices and its applications |
| title_sort | strong subadditivity for log-determinant of covariance matrices and its applications |
| url | https://eprints.nottingham.ac.uk/40789/ https://eprints.nottingham.ac.uk/40789/ https://eprints.nottingham.ac.uk/40789/ |