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

TL;DR

This paper proves a strong subadditivity inequality for the log-determinant of covariance matrices in quantum systems, revealing new limitations on information distribution and monogamy constraints in Gaussian states.

Contribution

It establishes a novel strong subadditivity inequality for covariance matrices, stronger than von Neumann entropy inequalities in certain quantum states, with implications for quantum correlations.

Findings

Proves strong subadditivity for covariance matrices in quantum systems

Shows the inequality is stronger than von Neumann entropy inequalities in some Gaussian states

Derives monogamy constraints for EPR steerability in multimode systems

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.