Schur complement inequalities for covariance matrices and monogamy of quantum correlations
We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entang...
| Main Authors: | , , , |
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| Format: | Article |
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American Physical Society
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40781/ |
| _version_ | 1848796132363206656 |
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| author | Lami, Ludovico Hirche, Christoph Adesso, Gerardo Winter, Andreas |
| author_facet | Lami, Ludovico Hirche, Christoph Adesso, Gerardo Winter, Andreas |
| author_sort | Lami, Ludovico |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entanglement and steering quantifiers in continuous variable systems with an arbitrary number of modes per party. A powerful hierarchical relation for correlation measures based on the log-determinant of covariance matrices is further established for all Gaussian states, which has no counterpart among quantities based on the conventional von Neumann entropy. |
| first_indexed | 2025-11-14T19:43:07Z |
| format | Article |
| id | nottingham-40781 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:07Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-407812020-05-04T18:20:13Z https://eprints.nottingham.ac.uk/40781/ Schur complement inequalities for covariance matrices and monogamy of quantum correlations Lami, Ludovico Hirche, Christoph Adesso, Gerardo Winter, Andreas We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entanglement and steering quantifiers in continuous variable systems with an arbitrary number of modes per party. A powerful hierarchical relation for correlation measures based on the log-determinant of covariance matrices is further established for all Gaussian states, which has no counterpart among quantities based on the conventional von Neumann entropy. American Physical Society 2016-11-23 Article PeerReviewed Lami, Ludovico, Hirche, Christoph, Adesso, Gerardo and Winter, Andreas (2016) Schur complement inequalities for covariance matrices and monogamy of quantum correlations. Physical Review Letters, 117 . 220502/1-220502/6. ISSN 1079-7114 http://dx.doi.org/10.1103/PhysRevLett.117.220502 doi:10.1103/PhysRevLett.117.220502 doi:10.1103/PhysRevLett.117.220502 |
| spellingShingle | Lami, Ludovico Hirche, Christoph Adesso, Gerardo Winter, Andreas Schur complement inequalities for covariance matrices and monogamy of quantum correlations |
| title | Schur complement inequalities for covariance matrices and monogamy of quantum correlations |
| title_full | Schur complement inequalities for covariance matrices and monogamy of quantum correlations |
| title_fullStr | Schur complement inequalities for covariance matrices and monogamy of quantum correlations |
| title_full_unstemmed | Schur complement inequalities for covariance matrices and monogamy of quantum correlations |
| title_short | Schur complement inequalities for covariance matrices and monogamy of quantum correlations |
| title_sort | schur complement inequalities for covariance matrices and monogamy of quantum correlations |
| url | https://eprints.nottingham.ac.uk/40781/ https://eprints.nottingham.ac.uk/40781/ https://eprints.nottingham.ac.uk/40781/ |