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Abstract: According to Hudson-s theorem, any pure quantum state with a positive Wignerfunction is necessarily a Gaussian state. Here, we make a step towards theextension of this theorem to mixed quantum states by finding upper and lowerbounds on the degree of non-Gaussianity of states with positive Wignerfunctions. The bounds are expressed in the form of parametric functionsrelating the degree of non-Gaussianity of a state, its purity, and the purityof the Gaussian state characterized by the same covariance matrix. Although ourbounds are not tight, they permit us to visualize the set of states withpositive Wigner functions.



Author: A. Mandilara, E. Karpov, N. J. Cerf

Source: https://arxiv.org/



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