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Journal of Modern Optics

Entangled non-Gaussian states formed by mixing Gaussian states

Austin P. Lund, Timothy C. Ralph, Peter van Loock

Published Jul 18, 2008• 6 citations
Publisher

Abstract

We study a class of non-Gaussian mixed states formed from the random mixture of a two-mode squeezed vacuum and a standard vacuum state. These states are a representative example of a broad class of non-Gaussian entangled states. We show that although these states are closely related to Gaussian entangled states, they exhibit distinct properties previously only associated with more exotic, pure non-Gaussian states.

DOI
10.1080/09500340801986932

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We study the measurement-induced non-Gaussian operation on the single- and two-mode Gaussian squeezed vacuum states with beam splitters and on-off type photon detectors, with which mixed non-Gaussian states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are effectively suppressed and enhanced, respectively. To investigate an operational meaning of these states, especially entangled states, we also evaluate the quantum dense coding scheme from the viewpoint of the mutual information, and we show that non-Gaussian entangled state can be advantageous compared with the original two-mode squeezed state.
We study the measurement-induced non-Gaussian operation on the single- and two-mode \\textit{Gaussian} squeezed vacuum states with beam splitters and on-off type photon detectors, with which \\textit{mixed non-Gaussian} states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are effectively suppressed and enhanced, respectively. To investigate an operational meaning of these states, especially entangled states, we also evaluate the quantum dense coding scheme from the viewpoint of the mutual information, and we show that non-Gaussian entangled state can be advantageous compared with the original two-mode squeezed state.
Inspired by the definition of the non-Gaussian two-parametric continuous-variable analog of an isotropic state introduced by Mi\ifmmode \check{s}\else \v{s}\fi{}ta 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.