Bell inequality for pairs of particle-number-superselection-rule restricted states

TL;DR

This paper introduces a new Bell inequality for systems with superselection rules, enabling detection of mode entanglement in massive particles where previous inequalities failed, though violations decrease with more particles.

Contribution

A novel Bell inequality that bypasses superselection rules using pairs of states, applicable to mode entanglement of massive particles, and feasible with current experimental techniques.

Findings

Detects entanglement where other inequalities fail

Violation decreases as particle number increases

Can be implemented with existing experimental methods

Abstract

Proposals for Bell inequality tests on systems restricted by superselection rules often require operations that are difficult to implement in practice. In this paper, we derive a new Bell inequality, where pairs of states are used to by-pass the superselection rule. In particular, we focus on mode entanglement of an arbitrary number of massive particles and show that our Bell inequality detects the entanglement in the pair when other inequalities fail. However, as the number of particles in the system increases, the violation of our Bell inequality decreases due to the restriction in the measurement space caused by the superselection rule. This Bell test can be implemented using techniques that are routinely used in current experiments.