Tomographic Universality of the Discrete Wigner Function

Author:

Sainz Isabel1ORCID,Camacho Ernesto2ORCID,García Andrés2ORCID,Klimov Andrei B.1ORCID

Affiliation:

1. Departamento de Física, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, Mexico

2. Departamento de Matemáticas, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, Mexico

Abstract

We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),Astronomy and Astrophysics,Atomic and Molecular Physics, and Optics,Statistical and Nonlinear Physics

Reference43 articles.

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