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Non-negative Wigner functions in prime dimensions

David Gross
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Abstract

According to a classical result due to Hudson, the Wigner function of a pure, continuous variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum systems. In this context, the role of Gaussian states is taken on by stabilizer states. The general results have been published in [D. Gross, J. Math. Phys. 47, 122107 (2006)]. For the case of systems of odd prime dimension, a greatly simplified proof can be employed which still exhibits the main ideas. The present paper gives a self-contained account of these methods.

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David Gross. 2007-01-31. Non-negative Wigner functions in prime dimensions. https://doi.org/10.1007/s00340-006-2510-9

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