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Schur complement inequalities for covariance matrices and monogamy of quantum correlations

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

Authors

Ludovico Lami

Christoph Hirche

Andreas Winter



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.

Journal Article Type Article
Publication Date Nov 23, 2016
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
APA6 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, https://doi.org/10.1103/PhysRevLett.117.220502
DOI https://doi.org/10.1103/PhysRevLett.117.220502
Publisher URL http://dx.doi.org/10.1103/PhysRevLett.117.220502
Related Public URLs https://arxiv.org/abs/1607.05285
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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