Gaussian continuous-variable isotropic state

Inspired by the definition of the non-Gaussian two-parametric continuous-variable analog of an isotropic state introduced by Mista et al. [Phys. Rev. A 65, 062315 (2002)], 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 analog 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 an entangled pure state with additional Gaussian noise controlled by a mixing probability. Using various entanglement criteria and measures, we study the nonclassical 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.

Automated summary

Inspired by a previously introduced non-Gaussian two-parametric continuous-variable analog of an isotropic state, the study proposes a simple yet interesting Gaussian analog of an isotropic state with a correlation structure controlled by a mixing probability. Different from conventional isotropic states, the Gaussian version here is defined by a convex combination of covariance matrices and exhibits a finite threshold for entanglement in the parameter space, similar to the finite-dimensional two-qubit isotropic state.