Many-body Bell inequalities for bosonic qubits

TL;DR

This paper develops a method to analyze Bell inequalities in many-body bosonic systems, enabling the study of quantum correlations in complex setups like Bose-Einstein condensates and photon pairs, regardless of particle number constraints.

Contribution

It introduces a step-by-step approach to study many-body Bell correlations in bosonic qubits, applicable to systems with fixed or variable particle numbers.

Findings

Method successfully analyzes Bell correlations in two-mode Bose-Einstein condensates.

Applicable to both fixed and non-fixed particle number scenarios.

Enhances understanding of quantum nonlocality in many-body bosonic systems.

Abstract

Since John Bell formulated his paramount inequality for a pair of spin-$1/2$ particles, quantum mechanics has been confronted with the postulates of local realism with various equivalent configurations. Current technology, with its advanced manipulation and detection methods, allows to extend the Bell tests to more complex structures. The aim of this work is to analyze a set of Bell inequalities suitable for a possibly broad family of many-body systems with the focus on bosonic qubits. We develop a method that allows for a step-by-step study of the many-body Bell correlations, for instance among atoms forming a two-mode Bose-Einstein condensate or between photons obtained from the parametric-down conversion. The presented approach is valid both for cases of fixed and non-fixed number of particles, hence it allows for a thorough analysis of quantum correlations in a variety of many-body systems.