Strong subadditivity for log-determinant of covariance matrices and its applications

Adesso, Gerardo; Simon, R.

Abstract

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.

• Journal Article Type: Article
• Acceptance Date: Jul 4, 2016
• Online Publication Date: Jul 22, 2016
• Publication Date: Jul 22, 2016
• Deposit Date: Feb 24, 2017
• Publicly Available Date: Feb 24, 2017
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 49
• Issue: 34
• Article Number: 34LT02
• DOI: https://doi.org/10.1088/1751-8113/49/34/34LT02
• Public URL: https://nottingham-repository.worktribe.com/output/799779
• Publisher URL: http://iopscience.iop.org/article/10.1088/1751-8113/49/34/34LT02/meta;jsessionid=43AE706290A778E5437CC22026CDAA2E.c2.iopscience.cld.iop.org
• Related Public URLs: https://arxiv.org/abs/1601.03226
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1751-8113/49/34/34LT02.