Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2

TL;DR

This paper shows that Renyi-2 entropy effectively measures information and correlations in Gaussian quantum states, satisfying key properties like strong subadditivity and enabling analysis of entanglement and quantum correlations.

Contribution

It introduces Renyi-2 entropy as a natural measure for Gaussian states, proving its strong subadditivity and applying it to quantify entanglement and correlations.

Findings

Renyi-2 entropy satisfies strong subadditivity for Gaussian states

The measure can quantify Gaussian entanglement and correlations

Properties like monogamy are satisfied by the proposed measures

Abstract

We demonstrate that the Renyi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.