Entangled state for constructing generalized phase space representation and its statistical behavior

TL;DR

This paper introduces a generalized phase space representation based on entangled states, providing a complete, non-orthogonal basis with clear statistical interpretation and demonstrating its minimum uncertainty properties.

Contribution

It constructs a new phase space representation using entangled states, linking quantum entanglement with statistical and uncertainty properties in a novel way.

Findings

Derived the Weyl ordered form of the entangled state density operator

Established the statistical behavior of the marginal distribution

Demonstrated the minimum uncertainty relation for the entangled state

Abstract

Based on the conception of quantum entanglement of Einstein-Podolsky-Rosen we construct generalized phase space representation associated with the entangled state |Gamma>_{e}, which is endowed with definite physical meaning. The set of states make up a complete and non-orthogonal representation. The Weyl ordered form of |Gamma>_{ee}_<Gamma| is derived which clearly exhibit the statistical behavior of marginal distribution of |Gamma>_{ee}_<Gamma|.The minimum uncertainty relation obeyed by |Gamma>_{e} is also demonstrated.