Entropic characterization of Separability in Gaussian states

TL;DR

This paper investigates the separability of bipartite Gaussian states using the Abe-Rajagopal q-conditional entropy, demonstrating that this entropic measure provides stricter criteria than von Neumann entropy, especially in the limit as q approaches infinity.

Contribution

It introduces an entropic approach based on AR q-conditional entropy for assessing Gaussian state separability, extending the criteria beyond traditional methods.

Findings

AR q-conditional entropy offers stricter separability conditions than von Neumann entropy.

The approach is effective compared to the partial transpose criterion.

Illustrative examples confirm the method's applicability to physically relevant states.

Abstract

We explore separability of bipartite divisions of mixed Gaussian states based on the positivity of the Abe-Rajagopal (AR) q-conditional entropy. The AR q-conditional entropic characterization provide more stringent restrictions on separability (in the limit q tending to infinity) than that obtained from the corresponding von Neumann conditional entropy (q = 1 case)--similar to the situation in finite dimensional states. Effectiveness of this approach, in relation to the results obtained by partial transpose criterion, is explicitly analyzed in three illustrative examples of two-mode Gaussian states of physical significance.