POSITIVIZATION AND REGULARIZATION OF QUANTUM PHASE-SPACE DISTRIBUTIONS

It is shown that, to any quasiprobability distribution corresponding t o a given density operator, one can associate a class of positive dist ributions in an extended space. In situations where the quasiprobabili ty distributions are singular, these distributions are shown to provid e regularized versions thereof. The positive distribution introduced b y Drummond and Gardiner in the context of the Glauber-Sudarshan P-repr esentation is shown to arise as a special case. One can thus associate a positive distribution to the Wigner function such that its moments give the averages of Weyl-ordered operators with respect to the given density operator. It is also found that one can associate to the Glaub er-Sudarshan P-function, a distribution in the extended space which, t hough not positive, interestingly, involves the Wigner function. A mea surement scheme which directly yields these positive distributions is presented.