Quantum non-Gaussianity and quantification of nonclassicality

Abstract

The algebraic quantification of nonclassicality, which naturally arises from the quantum superposition principle, is related to properties of regular nonclassicality quasiprobabilities. The latter are obtained by non-Gaussian filtering of the Glauber-Sudarshan $P$~function. They yield lower bounds for the degree of nonclassicality. We also derive bounds for convex combinations of Gaussian states for certifying quantum non-Gaussianity directly from the experimentally accessible nonclassicality quasiprobabilities. Other quantum-state representations, such as $s$-parametrized quasiprobabilities, insufficiently indicate or even fail to directly uncover detailed information on the properties of quantum states. As an example, our approach is applied to multi-photon-added squeezed vacuum states.

arXiv comment8 pages, 6 figures

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• Nonclassical Light and Metrological Power: An Introductory Review
• Faithful hierarchy of genuine $n$-photon quantum non-Gaussian light
• Negativity of quasiprobability distributions as a measure of nonclassicality
• Quasiprobability distributions for quantum-optical coherence and beyond
• Sub-Planck structures and sensitivity of the superposed photon-added or photon-subtracted squeezed-vacuum states
• Nonclassicality detection from few Fock-state probabilities
• Dissipative evolution of quantum Gaussian states
• Direct experimental certification of quantum non-Gaussian character and Wigner function negativity of single-photon detectors
• Quasistates and quasiprobabilities
• Efficient construction of witnesses of stellar rank of nonclassical states of light
• Non-Gaussian entanglement swapping
• Verifying single-mode nonclassicality beyond negativity in phase space
• Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state
• Preparation of arbitrary quantum states with regular $P$~functions
• Detecting Nonclassicality and quantum non-Gaussianity of photon subtracted displaced Fock state
• Quantum effects of operator time ordering in the nonlinear Jaynes-Cummings model
• Certification of stellar ranks of quantum states of light with a pair of click detectors
• Detecting nonclassicality and non-Gaussianity of a coherent superposed quantum state