# A measure of non-Gaussianity for quantum states

A measure of non-Gaussianity for quantum states 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# A measure of non-Gaussianity for quantum states

Quantum Information Processing, Volume 11 (3) – Oct 19, 2011
20 pages

/lp/springer_journal/a-measure-of-non-gaussianity-for-quantum-states-SNYwyBtGml
Publisher
Springer Journals
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematics, general; Quantum Physics; Physics, general; Computer Science, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0314-2
Publisher site
See Article on Publisher Site

### 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.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 19, 2011

### References

• Quantum information with Gaussian states
Wang, X.-B.; Hiroshima, T.; Tomita, A.; Hayashi, M.

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