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

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.