Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

Details Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

2001-08-10

arxiv.org/abs/quant-ph/0108050v1

Phys.Rev. A 65(2002)032105

Physics

Quantum Physics

18 pages

Scientific paper

10.1103/PhysRevA.65.032105

In order to determine the Wigner function uniquely, we introduce a new condition which ensures that the Wigner function has correct marginal distributions along tilted lines. For a system in $N$ dimensional Hilbert space, whose "phase space" is a lattice with $N^2$ sites, we get different results depending on whether $N$ is odd or even. Under the new condition, the Wigner function is determined if $N$ is an odd number, but it does not exist if $N$ is even.

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