Single-particle Bell-type Inequality

TL;DR

This paper derives a Bell-type inequality for a single particle with two correlated spin states at different times, and demonstrates its violation by quantum predictions, challenging classical notions of locality.

Contribution

It introduces a novel single-particle Bell inequality for sequential states and shows quantum mechanics can violate it, even without locality assumptions.

Findings

Quantum predictions violate the derived inequality.

The inequality applies to sequential measurements on a single particle.

Violations occur regardless of locality assumptions.

Abstract

It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle. Here, we derive a single-particle Bell's inequality for two correlated spin states at two successive times, appealing to the statistical independence condition in an ideal experiment, for a locally causal hidden variables theory. We show that regardless of the locality assumption, the inequality can be violated by some quantum predictions.