Measures of non-Gaussianity for one-mode field states

Abstract

We introduce and investigate a distance-type measure of non-Gaussianity based on the quantum fidelity. This new measure can readily be evaluated for all pure states and mixed states that are diagonal in the Fock basis. In particular, for an $M$-photon added thermal state, an analysis of the Bures degree of non-Gaussianity is made in comparison with two previous measures built with the Hilbert-Schmidt metric and the relative entropy. We obtain a compact analytic formula for the Hilbert-Schmidt non-Gaussianity measure and find a good consistency of the three examined measures.

Submitted to Physica Scripta as a contribution to CEWQO, Sinaia, Romania, 2012

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• Revealing quantum correlation by negativity of the Wigner function
• Loss of non-Gaussianity for damped photon-subtracted thermal states
• Simulating the Photon Statistics of Multimode Gaussian States by Automatic Differentiation of Generating Functions
• Quantum speed of evolution in a Markovian bosonic environment
• Modification of polarization through de-Gaussification
• Estimation of the set of states obtained in particle number measurement schemes
• Non-classical non-Gaussian state of a mechanical resonator via selectively incoherent damping in three-mode optomechanical systems
• Non-negative Wigner-like distributions and Renyi-Wigner entropies of arbitrary non-Gaussian quantum states: The thermal state of the one-dimensional box problem