Abstract
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 $s$-parametrized quasiprobability functions, generalizing previous criteria based on the Wigner function. In particular, we discuss in detail and analyze the properties of Husimi $Q$-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.
Highlights
The classification of quantum states of the harmonic oscillator according to classical vs nonclassical and Gaussian vs non-Gaussian paradigms has been an ongoing focus of research in quantum information for some time
We apply these results to the case of s-parametrized quasiprobability distributions, generalizing the criteria obtained in [36] for the Wigner function, to the Husimi Q function (s = −1) and in general to any distribution characterized by a parameter s < 0
We have presented a general method to derive bounds of linear functionals on the Gaussian convex hull
Summary
The classification of quantum states of the harmonic oscillator according to classical vs nonclassical and Gaussian vs non-Gaussian paradigms has been an ongoing focus of research in quantum information for some time now. In [35,36] the first attempt to detect quantum non-Gaussianity was pursued, by deriving witnesses based, respectively, on photon-number probabilities and on the Wigner function. We here present a framework to derive quantum nonGaussianity (QNG) witnesses based on generic linear functionals. We apply these results to the case of s-parametrized quasiprobability distributions, generalizing the criteria obtained in [36] for the Wigner function, to the Husimi Q function (s = −1) and in general to any distribution characterized by a parameter s < 0.
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