Schur complement inequalities for covariance matrices and monogamy of quantum correlations

Lami, Ludovico; Hirche, Christoph; Adesso, Gerardo; Winter, Andreas

Abstract

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.

Citation

Lami, L., Hirche, C., Adesso, G., & Winter, A. (2016). Schur complement inequalities for covariance matrices and monogamy of quantum correlations. Physical Review Letters, 117, Article 220502. https://doi.org/10.1103/PhysRevLett.117.220502

• Journal Article Type: Article
• Acceptance Date: Nov 23, 2016
• Publication Date: Nov 23, 2016
• Deposit Date: Feb 24, 2017
• Publicly Available Date: Feb 24, 2017
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 117
• Article Number: 220502
• DOI: https://doi.org/10.1103/PhysRevLett.117.220502
• Public URL: https://nottingham-repository.worktribe.com/output/827311
• Publisher URL: http://dx.doi.org/10.1103/PhysRevLett.117.220502
• Related Public URLs: https://arxiv.org/abs/1607.05285
• Contract Date: Feb 24, 2017