New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

TL;DR

This paper introduces a new two-fold complex integration transformation for the Wigner operator in phase space quantum mechanics, specifically addressing the two-mode entangled case, which helps solve operator ordering problems.

Contribution

It extends Fan's work by deriving a novel transformation and its inverse for the entangled Wigner operator using Weyl ordering and bipartite entangled states.

Findings

Derived a new two-fold complex integration transformation for the entangled Wigner operator.

Provided the inverse transformation to facilitate operator ordering.

Enhanced the mathematical tools available for phase space quantum mechanics.

Abstract

As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation about the Wigner operator (in its entangled form) in phase space quantum mechanics and its inverse transformation. In this way, some operator ordering problems can be solved and the contents of phase space quantum mechanics can be enriched.