Nonclassicality Invariant of General Two-Mode Gaussian States

TL;DR

This paper introduces a new invariant measure for nonclassicality in two-mode Gaussian states, revealing how entanglement and local nonclassicality can be interconverted, with applications to twin beams and extensions to three-mode states.

Contribution

A novel nonclassicality invariant for two-mode Gaussian states that decomposes into entanglement and local nonclassicality components, enabling analysis of state transformations.

Findings

Invariant remains unchanged under photon-number preserving unitaries.

Entanglement can be converted into local squeezing and vice versa.

Application to twin beams demonstrates the invariant's utility.

Abstract

We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given.