Separability criteria for continuous variable systems

TL;DR

This paper introduces a new separability criterion for continuous variable two-party quantum systems based on second moment analysis, which is more stringent than previous criteria and helps better identify entanglement.

Contribution

A novel separability condition for continuous variable systems derived without relying on the non-negativity of the partially transposed density matrix, establishing a hierarchy of criteria.

Findings

New criterion is more stringent than Simon's criterion.

When combined with squeezing, criteria become equivalent at the P-representation boundary.

The hierarchy of criteria effectively analyzes Gaussian system separability.

Abstract

A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the non-negativity of the partially transposed density matrix. This separability criterion is generally more stringent than that used by Simon which is based on the non-negativity of partially transposed density matrix, and thus this criterion may be useful in the analysis of general continuous two-party systems. Another separability criterion used by Duan et al. is shown to be generally weaker than that of Simon. We thus have a hierarchy of separability criteria, but all these criteria when combined with suitable squeezing become equivalent at the boundary of the P-representation condition and thus turned out to be sufficient to analyze the separability of two-party Gaussian systems.