Segal-Bargmann type spaces related to non-rotational measure, and entanglement of bipartite squeezed coherent states

TL;DR

This paper explores the relationship between squeezing and entanglement in bipartite quantum states using phase-space methods, revealing how non-rotational measures influence entanglement quantification.

Contribution

It introduces a novel phase-space approach based on holomorphic Hermite functions to analyze entanglement in bipartite squeezed states, linking non-rotational measures to squeezing parameters.

Findings

Orthogonality of holomorphic Hermite functions relates non-rotational measure to squeezing.

Phase-space Peres-Horodecki criterion effectively detects entanglement.

Log-negativity quantifies the degree of entanglement.

Abstract

Entanglement of bipartite squeezed states generated by holomorphic Hermite functions of two complex variables is investigated using phase-space approach based on the Wigner distribution function. Orthogonality of the holomorphic Hermite functions implies the relationship between certain real parameter associated with the non-rotational measure in the Bargmann space and the squeezing parameter. The mutual relation between squeezing and entanglement is elucidated with the help of Peres-Horodecki positive partial transpose criterion formulated in the phase-space version for continuous-variable systems. The quantitative characteristics of the entanglement is determined using the log-negativity criterion. The oscillator-like model of a two-particle quantum-mechanical system is developed to illustrate the presented findings.