Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

TL;DR

This paper introduces a new class of generalized squeezing operators based on su(1,1) algebra, explores their impact on bipartite Wigner functions, and provides a way to quantify entanglement using Wehrl's entropy functionals.

Contribution

It presents a novel class of unitary transformations generalizing squeezing in quantum optics and develops a framework to analyze bipartite entanglement via phase-space entropy measures.

Findings

New generalized squeezing operators based on su(1,1) algebra.

Derived bipartite Wigner function expression revealing two entanglement sources.

Quantitative entanglement estimates using Wehrl's entropy functionals.

Abstract

We introduce a new class of unitary transformations based on the su(1,1) Lie algebra that generalizes, for certain particular representations of its generators, well-known squeezing transformations in quantum optics. To illustrate our results, we focus on the two-mode bosonic representation and show how the parametric amplifier model can be modified in order to generate such a generalized squeezing operator. Furthermore, we obtain a general expression for the bipartite Wigner function which allows us to identify two distinct sources of entanglement, here labelled by dynamical and kinematical entanglement. We also establish a quantitative estimate of entanglement for bipartite systems through some basic definitions of entropy functionals in continuous phase-space representations.