Phys. Rev. Lett. 83, 3758–3761 (1999)Bounds on Integrals of the Wigner FunctionReceived 11 May 1999; revised 19 August 1999; published in the issue dated 8 November 1999 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 1 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 a 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. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.83.3758
DOI:
10.1103/PhysRevLett.83.3758
PACS:
03.65.Bz, 32.90.+a, 42.50.Dv, 42.50.Vk
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