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A measure of non-Gaussianity for quantum states

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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 \({Q(\alpha),\alpha\in\mathcal{C}^n}\) . 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) → λ2n 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.

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Authors and Affiliations

  1. Raman Research Institute, C. V. Raman Avenue, Sadashivanagar, Bangalore, 560 080, India

    J. Solomon Ivan

  2. S.N. Bose National Centre for Basic Sciences, Sector-III, Block-JD, Salt Lake, Kolkata, 700 098, India

    M. Sanjay Kumar

  3. Optics and Quantum Information Group, The Institute of Mathematical Sciences, C.I.T Campus, Tharamani, Chennai, 600 113, India

    R. Simon

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  1. J. Solomon Ivan
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  3. R. Simon
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Correspondence to R. Simon.

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Ivan, J.S., Kumar, M.S. & Simon, R. A measure of non-Gaussianity for quantum states. Quantum Inf Process 11, 853–872 (2012). https://doi.org/10.1007/s11128-011-0314-2

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