Extending Hudson's theorem to mixed quantum states
Name
Mandilara-2009-Extending Hudson's t.pdf
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Author(s)
Mandilara, Aikaterini
Karpov, Evgueni
Cerf, Nicolas J.
Date Issued
June 2009
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
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.
MIT Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.79.062302
