Extending Hudson's theorem to mixed quantum states
Author(s)Mandilara, Aikaterini; Karpov, Evgueni; Cerf, Nicolas J.
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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.
DepartmentMassachusetts Institute of Technology. Research Laboratory of Electronics
Physical Review A
American Physical Society
Mandilara, A., E. Karpov, and N. Cerf. “Extending Hudson’s Theorem to Mixed Quantum States.” Physical Review A 79.6 (2009) : [4 pages]. © 2009 The American Physical Society.
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