Gaussian Continuous-Variable Isotropic State

TL;DR

This paper introduces a Gaussian analogue of the isotropic state in continuous-variable quantum systems, analyzing its entanglement properties and correlation structure, revealing a finite entanglement threshold similar to finite-dimensional isotropic states.

Contribution

It proposes a Gaussian version of the isotropic state as an independent state, providing insights into its entanglement behavior and correlation structure, which was not previously studied.

Findings

Gaussian isotropic state has a finite entanglement threshold

Exhibits similar phenomenology to two-qubit isotropic states

Contains non-classical correlations analyzed via entanglement measures

Abstract

Inspired by the definition of the non-Gaussian two-parametric continuous variable analogue of an isotropic state introduced by Mi\v{s}ta et al. [Phys. Rev. A, 65, 062315 (2002); arXiv:quant-ph/0112062], we propose to take the Gaussian part of this state as an independent state by itself, which yields a simple, but with respect to the correlation structure interesting example of a two-mode Gaussian analogue of an isotropic state. Unlike conventional isotropic states which are defined as a convex combination of a thermal and an entangled density operator, the Gaussian version studied here is defined by a convex combination of the corresponding covariance matrices and can be understood as entangled pure state with additional Gaussian noise controlled by a mixing probability. Using various entanglement criteria and measures, we study the non-classical correlations contained in this state. Unlike the previously studied non-Gaussian two-parametric isotropic state, the Gaussian state considered here features a finite threshold in the parameter space where entanglement sets in. In particular, it turns out that it exhibits an analogous phenomenology as the finite-dimensional two-qubit isotropic state.