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Classicality in discrete Wigner functions

Cecilia Cormick·Ernesto F. Galvao·Daniel Gottesman·Juan Pablo Paz·Arthur O. Pittenger
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Abstract

Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by one of us [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.

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Cecilia Cormick, Ernesto F. Galvao, Daniel Gottesman, Juan Pablo Paz, Arthur O. Pittenger. 2005-06-27. Classicality in discrete Wigner functions. https://doi.org/10.1103/physreva.73.012301

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