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Physics Today

Cosmic experiment is closing another Bell test loophole

Andrew Grant

Published Dec 1, 2016• 1 citation
Publisher

Abstract

Extra Dimensions: A new experiment combines nanoscale measurements and interstellar distances to demonstrate quantum nonlocality.
DOI
10.1063/pt.5.2051

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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.
Exhaustively identifying all loopholes in the Bell test is demanding for interpreting the results of the relevant experiments, since any loophole if not closed can be catastrophic to our understanding of the nonlocal structure of quantum mechanics. Despite a series of recent Bell experiments that claim to be free of loopholes, a united framework with a sound base is still missing to fully recognize all potential loopholes in these experiments, as verified by a recent experiment that has pinned down a detection loophole of a new type in Bell analysis. Here, we reveal another loophole previously unknown in the Bell test through a local theory developed here on the basis of a new mathematical concept of high-dimensional vectorial probability, quantified as a vector with interesting but hidden geometry in the probability space. We show that the statistical property of the stochastic events generated for the Bell test can be well described by the local theory, and, in particular, the correlations of these events that violate Bell's theorem can be closely connected to the geometry of the vectorial probability. To close the loophole, theoretical investigations are highly recommended to search for the statistical nature of the stochastic events in quantum measurements that can distinguish the predictions of quantum mechanics and those of the local theory.
Bell inequality tests based on high-dimensional entanglement usually require measurements that can resolve multiple possible outcomes. However, the implementation of high-dimensional multi-outcome measurements is often only emulated via a collection of ``click or no-click'' measurements. This reduction of multi-outcome measurements to binary-outcome measurements opens a loophole in high-dimensional tests Bell inequalities which can be exploited by local hidden variable models [Tavakoli et al., Phys. Rev. A 111, 042433 (2025)]. Here, we close this loophole by using four-dimensional photonic path-mode entanglement and multi-outcome detection. We test both the well-known Collins-Gisin-Linden-Massar-Popescu inequality and a related Bell inequality tailored for maximally entangled states in high-dimension. We observe violations that are large enough to also rule out any quantum model based on entanglement of lower dimension, thereby demonstrating genuinely high-dimensional nonlocality free of the binarisation loophole.