Bell Inequality Violations Without Entanglement? It's Just Postselection

TL;DR

This paper demonstrates that reported Bell inequality violations without entanglement are due to postselection effects, not genuine quantum nonlocality, by providing a classical analog and analyzing the role of statistical independence.

Contribution

The paper clarifies that Bell violations without entanglement are artifacts of postselection, emphasizing the importance of statistical independence assumptions.

Findings

Postselection can produce Bell violations in classical models.

Classical analog reproduces quantum experiment results.

Violations do not challenge local realism due to statistical independence rejection.

Abstract

Recently Wang et al. have reported a violation of a Bell inequality without entanglement [arXiv:2507.07756]. We show that their result is an artifact of postselection. It is well known that postselection may yield Bell inequality violations, both in classical toy models and in real experiments with delayed-choice entanglement-swapping. Here we describe a classical analog of Wang et al.'s experiment, and show that it produces essentially the same results as their quantum version. We explain in detail why neither version is a challenge to Local Causality or local realism: the postselection entails a rejection of Bell's assumption of Statistical Independence.