Positivity properties of phase-plane distribution functions

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Abstract

The aim of this paper is to compare the members of Cohen's class of phase-plane distributions with respect to positivity properties. It is known that certain averages (which are in a sense compatible with Heisenberg's uncertainty principle) of the Wigner distribution over the phase-plane yield non-negative values for all states. It is shown in this paper that the Wigner distribution is unique in this respect among the members of Cohen's class that have correct marginals or that satisfy Moyal's formula for all states. The subset of members of Cohen's class (not necessarily satisfying one of these two conditions) with positivity properties comparable with those for the Wigner distribution is shown to be rather small.
Original languageEnglish
Pages (from-to)2240-2252
Number of pages13
JournalJournal of Mathematical Physics
Volume25
Issue number7
DOIs
Publication statusPublished - 1984

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