Quasi-distributions for arbitrary non-commuting operators

• URL: http://arxiv.org/abs/2003.05509v1
• Date: Wed, 11 Mar 2020 20:15:26 GMT
• Title: Quasi-distributions for arbitrary non-commuting operators
• Authors: J. S. Ben-Benjamin, L. Cohen
• Abstract summary: We present a new approach for obtaining quantum quasi-probability distributions, $P(alpha,beta)$, for two arbitrary operators. We show that the quantum expectation value of an arbitrary operator can always be expressed as a phase space integral over $alpha$ and $beta$, where the integrand is a product of two terms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a new approach for obtaining quantum quasi-probability distributions, $P(\alpha,\beta)$, for two arbitrary operators, $\mathbf{a}$ and $\mathbf{b}$, where $\alpha$ and $\beta$ 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 $\alpha$ and $\beta$, 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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