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

Adesso, Gerardo and Simon, R. (2016) Strong subadditivity for log-determinant of covariance matrices and its applications. Journal of Physics A: Mathematical and Theoretical, 49 (34). 34LT02. ISSN 1751-8113

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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.

Item Type: Article
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
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
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Depositing User: Adesso, Gerardo
Date Deposited: 24 Feb 2017 09:54
Last Modified: 04 May 2020 17:59

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