Extending Hudson's theorem to mixed quantum states

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

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

According to Hudson's theorem, any pure quantum state with a positive Wigner function is necessarily a Gaussian state. Here, we make a step toward the extension of this theorem to mixed quantum states by finding upper and lower bounds on the degree of non-Gaussianity of states with positive Wigner functions. The bounds are expressed in the form of parametric functions relating the degree of non-Gaussianity of a state, its purity, and the purity of the Gaussian state characterized by the same covariance matrix. Although our bounds are not tight, they permit us to visualize the set of states with positive Wigner functions.

Original languageEnglish
Article number062302
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume79
Issue number6
DOIs
Publication statusPublished - Jun 3 2009

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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