Quasiprobabilities and Non-classical States

Abstract

Recall that a classical dynamical system may be described by a phase space probability distribution function f({q}, {p}), ({q}) ≡ q₁ q₂, ..., q _N ; {p} ≡ p₁, p₂, ..., p _N ) which is such that f({q}, {p})d^N qd^N p gives the probability that the system is in a volume element d^N qd^N p centered around ({q}, {p}). In the quantum mechanical description of a dynamical system, however, the phase space coordinates q _i and p _i can not be ascribed definite values simultaneously. Hence the concept of phase space distribution function does not exist for a quantum system. It is, however, possible to construct for a quantum system functions, called quasiprobability distributions (QPDs), resembling the classical phase space distribution functions. A QPD provides insight into quantum-classical correspondence as well as useful means of calculations.