A measure of non-Gaussianity for quantum states

Solomon Ivan, J. ; Sanjay Kumar, M. ; Simon, R. (2011) A measure of non-Gaussianity for quantum states Quantum Information Processing . pp. 1-20. ISSN 1570-0755

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Official URL: http://www.springerlink.com/content/d824737215gh51...

Related URL: http://dx.doi.org/10.1007/s11128-011-0314-2

Abstract

We propose a measure of non-Gaussianity for quantum states of a system of n oscillator modes. Our measure is based on the quasi-probability Q(α),α ∈ Cn . Since any measure of non-Gaussianity is necessarily an attempt at making a quantitative statement on the departure of the shape of the Q function from Gaussian, any good measure of non-Gaussianity should be invariant under transformations which do not alter the shape of the Q functions, namely displacements, passage through passive linear systems, and uniform scaling of all the phase space variables: Q(α)→λ 2n Q(λα). Our measure which meets this 'shape criterion' is computed for a few families of states, and the results are contrasted with existing measures of non-Gaussianity. The shape criterion implies, in particular, that the non-Gaussianity of the photon-added thermal states should be independent of temperature.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Non-gaussianity Measure; Quasiprobability; Q-function; Wehrl Entropy; Photon-added Thermal States
ID Code:87708
Deposited On:20 Mar 2012 15:12
Last Modified:20 Mar 2012 15:12

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