A critical appraisal of tests of locality and of entanglement versus non-entanglement at colliders

TL;DR

The paper critically analyzes the prospects for testing quantum locality and entanglement versus non-entanglement at collider experiments. It shows that spin correlations, which violate Bell-type inequalities in principle, cannot be accessed directly at colliders and must be inferred from angular distributions via spin-analyzing powers, which themselves rely on QM inputs. Consequently, any collider-based test of locality or entanglement requires presupposing QM/SM assumptions, invalidating a clean QM vs LHVT test in this setting. The authors also discuss direct measurements of spin-analyzing power, constraints on LHVTs, and the limits of using angular observables to exclude hidden-variable theories, reinforcing the no-go result while noting contexts where entanglement-inspired observables remain meaningful for SM tests. In short, current collider capabilities do not enable a logically coherent Bell/CHSH test of locality, though they may still illuminate SM structure through QM-inspired analyses.

Abstract

It has been argued more than 30 years ago that it is not possible to test locality at colliders, due to the inability to directly measure non-commutating observables such as spin components in current collider experiments. Recently, there has been a lot of phenomenological and experimental activity around testing locality via Bell-type experiments or entanglement versus non-entanglement in a collider environment. These results seem to evade the earlier no-go theorem by indirectly measuring spin correlations via their relation to angular correlations between momenta. We perform a careful study of the feasibility of such an approach. We scrutinize the relationship between spin and angular correlations in both quantum mechanics and local hidden variable theories. Our conclusion is that it is currently not possible to perform a logically coherent set of experimental measurements at colliders that would allow one to test locality or entanglement versus non-entanglement. This reaffirms the earlier no-go theorem. We stress that the no-go theorem does not apply to measurements of observables inspired from entanglement and Quantum Information Theory to test the Standard Model of particle physics.