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A family of Weyl-Wigner transforms for discrete variables defined in a finite-dimensional Hilbert space. (English) Zbl 1386.81109

Summary: We study the Weyl-Wigner transform in the case of discrete variables defined in a Hilbert space of finite prime-number dimensionality \(N\). We define a family of Weyl-Wigner transforms as function of a phase parameter. We show that it is only for a specific value of the parameter that all the properties we have examined have a parallel with the case of continuous variables defined in an infinite-dimensional Hilbert space. A geometrical interpretation is briefly discussed.

MSC:

81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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