Contextuality in bosonic bunching

TL;DR

This paper derives a non-contextual inequality for bosonic particles, shows it can be violated by quantum properties, and proposes using this violation as a test for bosonic nature.

Contribution

It introduces a new contextuality inequality for bosons and demonstrates its violation due to bosonic properties, offering a novel test for bosonic behavior.

Findings

The inequality is bounded by one under non-contextual assumptions.

Quantum mechanics with bosons can violate this bound up to 3/2.

Violation can serve as a test for bosonic nature.

Abstract

We show that under certain assumptions one can derive a variant of Specker's non-contextual inequality for a system of three indistinguishable bosonic particles. The inequality states that the sum of probabilities of three pairwise exclusive events is bounded by one. This inequality cannot be violated using standard quantum mechanical projectors. On the other hand, due to bosonic properties this bound is violated up to 3/2. We also argue that the violation of this inequality can be considered as a test of bosonic nature.