Spin squeezing and entanglement via finite-dimensional discrete phase-space description

TL;DR

This paper develops a discrete phase-space approach to analyze spin squeezing and entanglement in spin systems, applying it to the LMG model to explore quantum correlations and uncertainty relations.

Contribution

It introduces a novel algebraic framework using discrete phase-space mapping for spin systems, linking squeezing, entanglement, and correlations.

Findings

Demonstrates the connection between squeezing and entanglement effects.

Analyzes the time evolution of uncertainty and entanglement measures.

Provides insights into the role of spin correlations via quasiprobability functions.

Abstract

We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson-Schr\"{o}dinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects, as well as allow to investigate the basic role of spin correlations through the discrete representatives of quasiprobability distribution functions. Entropy functionals are also discussed in this context. The main sequence correlations -> entanglement -> squeezing of quantum effects embraces a new set of insights and interpretations in this framework, which represents an effective gain for future researches in different spin systems.