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Studies in History and Philosophy of Science Part A

Delayed-choice entanglement swapping experiments: No evidence for timelike entanglement

Jørn Kløvfjell Mjelva

Published May 22, 2024• 2 citations
Publisher

Abstract

In recent years, there has been a growing interest in the possibility of temporal nonlocality, mirroring the spatial nonlocality supposedly evidenced by the Bell correlations. In this context, Glick (2019) has argued that timelike entanglement and temporal nonlocality is demonstrated in delayed-choice entanglement swapping (DCES) experiments, like that of Ma et al. (2012), Megidish et al. (2013) and Hensen et al. (2015). I will argue that a careful analysis of these experiments shows that they in fact display nothing more than "ordinary" spacelike entanglement, and that any purported timelike entanglement is an artefact of selection bias. Regardless any other reason one may have for challenging the assumption of temporal locality, timelike entanglement as evidenced by these experiments is not among them. I conclude by discussing what lessons on the nature of entanglement might be drawn from an examination of DCES experiments.

DOI
10.1016/j.shpsa.2024.04.001

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In recent years, there has been a growing interest in the possibility of temporal nonlocality, mirroring the spatial nonlocality supposedly evidenced by the Bell correlations. In this context, Glick (2019) has argued that timelike entanglement and temporal nonlocality is demonstrated in delayed-choice entanglement swapping (DCES) experiments, like that of Ma et al. (2012), Megidish et al. (2013) and Hensen et al. (2015). I will argue that a careful analysis of these experiments shows that they in fact display nothing more than "ordinary" spacelike entanglement, and that any purported timelike entanglement is an artefact of selection bias. Regardless any other reason one may have for challenging the assumption of temporal locality, timelike entanglement as evidenced by these experiments is not among them. I conclude by discussing what lessons on the nature of entanglement might be drawn from an examination of DCES experiments.
We propose that quantum entanglement is a special sort of selection artefact, explicable as a combination of (i) collider bias and (ii) a boundary constraint on the collider variable. We show that the proposal is valid for a special class of (`W-shaped') Bell experiments involving delayed-choice entanglement swapping, and argue that it can be extended to the ordinary (`V-shaped') case. The proposal requires no direct causal influence outside lightcones, and may hence offer a way to reconcile Bell nonlocality and relativity. The main argument is a detailed version of an approach previously outlined in arXiv:2404.13928 [quant-ph].
Delayed-choice experiments in quantum mechanics are often taken to undermine a realistic interpretation of the quantum state.More specifically, Healey has recently argued that the phenomenon of delayed-choice entanglement swapping is incompatible with the view that entanglement is a physical relation between quantum systems.This paper argues against these claims.It first reviews two paradigmatic delayed-choice experiments and analyzes their metaphysical implications.It then applies the results of this analysis to the case of entanglement swapping, showing that such experiments pose no threat to realism about entanglement.
A 2015 experiment by Hanson and Delft colleagues provided new confirmation that the quantum world violates the Bell inequalities, being the first Bell test to close two known experimental loopholes simultaneously. The experiment was also taken to provide new evidence of quantum nonlocality. Here we argue for caution about the latter claim. The Delft experiment relies on entanglement swapping, and our main claim is that this geometry introduces new loopholes in the argument from violation of the Bell inequalities to nonlocality. In the absence of retrocausality, the sensitivity of such experiments to these new loopholes depends on the temporal relation between the entanglement swapping measurement C and the two measurements A and B between which we seek to infer nonlocality. The loopholes loom large if the C is in the future of A and B, but not if C is in the past. The Delft experiment itself is the intermediate case, in which the separation is spacelike. We argue that this leaves it vulnerable to the new loopholes, unable to establish conclusively that it avoids them. We also discuss the implications of permitting retrocausality for the issue of causal influence across entanglement swapping measurements.
Experiments demonstrating entanglement swapping have been alleged to challenge realism about entanglement. Seevinck (2006) claims that entangle- ment “cannot be considered ontologically robust” while Healey (2012) claims that entanglement swapping “undermines the idea that ascribing an entangled state to quantum systems is a way of representing some new, non-classical, physical relation between them.” My aim in this paper is to show that realism is not threatened by the possibility of entanglement swapping, but rather, it should be informed by the phenomenon. I argue—expanding the argument of Timpson and Brown (2010)—that ordinary entanglement swapping cases present no new challenges for the realist. With respect to the delayed-choice variant discussed by Healey, I claim that there are two options available to the realist: (a) deny these are cases of genuine swapping (following Egg (2013)) or (b) allow for existence of entanglement between timelike separated regions. This latter option, while radical, is not incoherent and has been suggested in quite different contexts. While I stop short of claiming that the realist must take this option, doing so allows one to avoid certain costs associated with Egg’s “orthodox” account. I conclude by noting several important implication of entanglement swapping for how one thinks of entanglement generally.
Entanglement swapping between photons that never coexist in laboratory time provides a clean test of the temporal ordering of quantum measurements without invoking retrocausal signaling. We review the 2013 Physical Review Letters experiment by Megidish et al., correcting several common secondary-source simplifications: the temporal separation was implemented with a 31.6 m free-space delay line (105 ns), the final state of photons 1 and 4 was characterized by quantum-state tomography, and the reported result was a conditional entangled state with approximately 77% fidelity to the target Bell state rather than a standalone Bell-inequality test. We then integrate this experimental basis with a DQ-12 interpretation in which photonic excitations are modeled phenomenologically as phase modes of a higher-dimensional continuous state substrate. Within that interpretation, detection is treated as a local relaxation map, while the Bell-state projection on the intermediate photons is represented as a conditional phasebridging operation. Crucially, the standard quantum-mechanical account is sufficient for the observed experiment; DQ-12 is therefore presented not as a confirmed explanation but as an additional ontology that acquires scientific content only through differential, falsifiable predictions. We propose residual observables, delay-dependent tests, matched controls, and a null hypothesis that reduce the DQ-12 claim to an experimentally decidable extension.Keywords: entanglement swapping; temporal entanglement; Bell-state measurement; quantum-state tomography; timelike separation; DQ-12; phase connectivity; emergent time; quantum foundations.
The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the nonlocality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spacelike separation, but also to particles with timelike separation. In order to demonstrate these principles, we generated and fully characterized an entangled pair of photons that have never coexisted. Using entanglement swapping between two temporally separated photon pairs, we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed two-photon state demonstrates that entanglement can be shared between timelike separated quantum systems.