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arXiv:2508.13431

Bell Inequality Violations Without Entanglement? It's Just Postselection

K. B. Wharton, Huw Price

Published Aug 19, 2025• 0 citations
arXivHTMLPDF

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.

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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.
Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within nondeterminism, i.e., in the context of stochastic local realism.
It is shown that the data of the Hensen et al. Bell test experiment exhibits anomalous postselection that can fully account for the apparent violation of the CHSH inequality. A simulation of a local realist model implementing similar postselection is presented. The model produces an apparent violation of CHSH indistinguishable from that of the experiment. The experimental data also appears to violate no-signaling, and it is shown how postselection can produce an artifactual violation of no-signaling. The Hensen et al. experiment does not succeed in rejecting classical locality and therefore does not confirm quantum nonlocality.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.
Wang et al. [Science Advances, 1 Aug 2025 Vol 11, Issue 31] recently reported an experiment that they interpret as demonstrating a violation of Bell's inequality using unentangled photons. Such a claim is highly controversial, since it is well established that product states cannot surpass the bounds set by local hidden variable models. In this manuscript, we analyze the essential features of the experiment through simplified, idealized scenarios. Our analysis shows that the apparent violation of Bell's inequality originates from two key elements: postselection and an unconventional normalization procedure. These steps produce quantities that formally mimic Bell-type correlations but lack the operational meaning required in a genuine Bell test. We therefore argue that the reported violation does not demonstrate nonlocality without entanglement, but rather reflects a misinterpretation of otherwise valid and interesting multiphoton interference effects.
Abstract Seminal for the raising of the quantum information age and quintessential for a deep understanding of nature, Bell inequality violations are known for having provided a profound disruption to classical models of the physical world. Yet, their meaning is still debatable nowadays. An important point under dispute in this context concerns the relevance of realism. While some believe that a Bell inequality violation implies the manifestation of nonlocal aspects, others defend that it is the notion of realism that should be abandoned. The purpose of the present work is to shed some light on the matter by employing a formal definition of (ir)realism. Our strategy consists of (i) rephrasing Bell’s assumption of local causality in terms of more primitive hypotheses and (ii) assessing where the fundamental difficulties emerge when using the quantum formalism. We analyze the question posed in the title using two distinct approaches and assert that a positive answer is justifiable. Nevertheless, even in this scenario, it becomes evident that violations of locality cannot be avoided. As a byproduct of our approach, the connections of (ir)realism with both quantum steering and entanglement are also discussed.
A common problem in Bell-type experiments is the well-known detection loophole: if the detection efficiencies are not perfect and if one simply postselects the conclusive events, one might observe a violation of a Bell inequality, even though a local model could have explained the experimental results. In this paper, we analyze the set of all postselected correlations that can be explained by a local model, and show that it forms a polytope, larger than the Bell local polytope. We characterize the facets of this postselected local polytope in the Clauser-Horne-Shimony-Holt scenario, where two parties have binary inputs and outcomes. Our approach gives interesting insights on the detection loophole problem.