Bounds on Integrals of the Wigner Function

Details Bounds on Integrals of the Wigner Function Bounds on Integrals of the Wigner Function

1999-05-28

arxiv.org/abs/quant-ph/9905097v2

Physics

Quantum Physics

10 pages, 1 PostScript figure, Latex file; revised following referees' comments; to appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.83.3758

The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over all possible states, reduces to the problem of finding the greatest and least eigenvalues of an hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.

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