Quasi-distributions for arbitrary non-commuting operators

We present a new approach for obtaining quantum quasi-probability distributions, $P(α,β)$, for two arbitrary operators, $\mathbf{a}$ and $\mathbf{b}$, where $α$ and $β$ are the corresponding c-variables. We show that the quantum expectation value of an arbitrary operator can always be expressed as a phase space integral over $α$ and $β$, where the integrand is a product of two terms: One dependent only on the quantum state, and the other only on the operator. In this formulation, the concepts of quasi-probability and correspondence rule arise naturally in that simultaneously with the derivation of the quasi-distribution, one obtains the generalization of the concept of correspondence rule for arbitrary operators.

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