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arXiv:1309.4221 · Physica Scripta

Detecting quantum non-Gaussianity of noisy Schrödinger cat states

Mattia L. Palma, Jimmy Stammers, Marco G. Genoni, Tommaso Tufarelli, Stefano Olivares, M S Kim, Matteo G. A. Paris

Published Apr 1, 2014• 6 citations
arXivHTMLPDF

Abstract

Highly quantum nonlinear interactions between different bosonic modes lead to the generation of quantum non-Gaussian states, i.e. states that cannot be written as mixtures of Gaussian states. A paradigmatic example is given by Schrödinger's cat states, that is, coherent superpositions of coherent states with opposite amplitude. We here consider a novel quantum non-Gaussianity criterion recently proposed in the literature and prove its effectiveness on Schrödinger cat states evolving in a lossy bosonic channel. We prove that the quantum non-Gaussianity can be effectively detected for high values of losses and for large coherent amplitudes of the cat states.

DOI
10.1088/0031-8949/2014/t160/014035

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Highly quantum nonlinear interactions between different bosonic modes lead to the generation of quantum non-Gaussian states, i.e. states that cannot be written as mixtures of Gaussian states. A paradigmatic example is given by Schrödinger's cat states, that is, coherent superpositions of coherent states with opposite amplitude. We here consider a novel quantum non-Gaussianity criterion recently proposed in the literature and prove its effectiveness on Schrödinger cat states evolving in a lossy bosonic channel. We prove that the quantum non-Gaussianity can be effectively detected for high values of losses and for large coherent amplitudes of the cat states.
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We address detection of quantum non-Gaussian states, i.e., nonclassical states that cannot be expressed as a convex mixture of Gaussian states, and present a method to derive a new family of criteria based on generic linear functionals. We then specialize this method to derive witnesses based on sss-parametrized quasiprobability functions, generalizing previous criteria based on the Wigner function. In particular, we discuss in detail and analyze the properties of Husimi QQQ-function-based witnesses and prove that they are often more effective than previous criteria in detecting quantum non-Gaussianity of various kinds of non-Gaussian states evolving in a lossy channel.
Non-Gaussian states, and specifically the paradigmatic cat state, are well known to be very sensitive to losses. When propagating through damping channels, these states quickly lose their nonclassical features and the associated negative oscillations of their Wigner function. However, by squeezing the superposition states, the decoherence process can be qualitatively changed and substantially slowed down. Here, as a first example, we experimentally observe the reduced decoherence of squeezed optical coherent-state superpositions through a lossy channel. To quantify the robustness of states, we introduce a combination of a decaying value and a rate of decay of the Wigner function negativity. This work, which uses squeezing as an ancillary Gaussian resource, opens new possibilities to protect and manipulate quantum superpositions in phase space.
Abstract We propose a method to faithfully probe and quantify the non-Gaussianity of single-mode fields in the coherent-state representations based on the averaged-cumulant technique. In comparison with the previous measure, S H Xiang et al (2018 Phys. Rev. A 97 042303), we characterize the non-Gaussianity of quantum states using the kurtosis of a Gaussian operator, rather than that of a quadrature operator. As applications, we investigate the non-Gaussianities of three different non-Gaussian states: a mixture of vacuum and Fock states, Schrödinger cat states, and photon-added coherent states. It is proven that such a kurtosis is a powerful and effective measure in appraising non-Gaussianity.
Abstract In this paper, we investigate the nonclassicality and non-Gaussianity of a coherent superposed quantum state (CSQS) which is obtained by applying a coherent superposition of field annihilation (a) and creation ( a † ) operators, N ( t a + r a † ) to a classical coherent state | α ⟩ , where t and r are scalars with t 2 + r 2 = 1 . Such an operation, when applied on states having classical characters, introduces strong nonclassicality. We use different criteria to check the nonclassicality and non-Gaussianity of the considered quantum state. We first compute the Wigner function of CSQS. To study the nonclassicality of the considered state we further use (a) linear entropy (b) Wigner logarithmic negativity and (c) skew information based measure. Relative entropy based measure is considered to analyze the variation in non-Gaussianity of CSQS. Finally, the dynamics of the Wigner function evolving under the photon loss channel is addressed to probe the effect of noise on nonclassicality as well as non-Gaussianity of CSQS.