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Extending Hudson's theorem to mixed quantum states

Author(s)
Mandilara, Aikaterini; Karpov, Evgueni; Cerf, Nicolas J.
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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.
Date issued
2009-06
URI
http://hdl.handle.net/1721.1/64931
Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
Journal
Physical Review A
Publisher
American Physical Society
Citation
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.
Version: Final published version
ISSN
1050-2947
1094-1622

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