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

TL;DR

This paper investigates how particle-number superselection rules affect quantum steering violations in indistinguishable particle systems, finding that violations are limited but can surpass Bell violations under certain conditions.

Contribution

It introduces a method to test steering inequality violations in superselection-restricted states using two copies, revealing their limitations and comparison with Bell violations.

Findings

Violations are higher than Bell inequality violations for the same states.

Superselection rules limit the maximum steering inequality violation.

Increasing particles in condensates decreases the violation amount.

Abstract

We consider violations of a Clauser-Horne-Shimony-Holt-type steering inequality for quantum states of systems of indistinguishable particles restricted by a particle-number-superselection rule. We check for violations in non-interacting Bose-Einstein condensate and N00N states, by using two copies of the states for bypassing the superselection rule. The superselection rule prevents the states from maximally violating the steering inequality. But the steering inequality violations are higher than Bell inequality violations for the same states. This in particular implies, in certain cases, that visibilities of the steering inequality violations are higher than the same for Bell inequality violations, for admixtures with white noise. We also found that an increase in the number of particles in the non-interacting condensate states results in a decrease of the violation amount of the steering inequality.