A measure of non-Gaussianity for quantum states

作者：Ivan J Solomon; Kumar M Sanjay; Simon R^*

来源：Quantum Information Processing, 2012, 11(3): 853-872.

DOI：10.1007/s11128-011-0314-2

• Non-Gaussianity measure
• Quasiprobability
• Q-function
• Wehrl entropy
• Photon-added thermal 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 is an element of 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(alpha) -> lambda(2n)Q(lambda alpha). 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.

• 出版日期2012-6
• 单位常州工学院