Schur complement inequalities for covariance matrices and monogamy of quantum correlations

Lami, Ludovico and Hirche, Christoph and 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

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1103/PhysRevLett.117.220502
Related URLs:
URLURL Type
https://arxiv.org/abs/1607.05285UNSPECIFIED
Depositing User: Adesso, Gerardo
Date Deposited: 24 Feb 2017 10:31
Last Modified: 25 Feb 2017 06:38
URI: http://eprints.nottingham.ac.uk/id/eprint/40781

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