Separability and entanglement of four-mode Gaussian states

TL;DR

This paper investigates the separability and entanglement of four-mode Gaussian states using criteria based on principal minors of the quadrature dispersion matrix, revealing that larger negative minors indicate higher entanglement.

Contribution

It demonstrates the sensitivity of principal minors to scaling parameters and empirically links their negativity to the degree of entanglement in Gaussian states.

Findings

Negative principal minors correlate with increased entanglement.

Scaling parameters influence the detection of entanglement.

Principal minors serve as indicators of state entanglement.

Abstract

The known Peres-Horodecki criterion and scaling criterion of separability are considered on examples of three-mode and four-mode Gaussian states of electromagnetic field. It is shown that the principal minors of the photon quadrature dispersion matrix are sensitive to the change of scaling parameters. An empirical observation has shown that the bigger the modulus of negative principal minors, the more entangled the state.