Optimizing entanglement and Bell inequality violation in top antitop events

Abstract

A top quark and an antitop quark produced together at colliders have correlated spins. These spins constitute a quantum state that can exhibit entanglement and violate Bell’s inequality. In realistic collider experiments, most analyses allow the axes, as well the Lorentz frame, to vary event by event, thus introducing a dependence on the choice of event-dependent basis leading us to adopt “fictitious states,” rather than genuine quantum states. The basis dependence of fictitious states allows for an optimization procedure, which makes the usage of fictitious states advantageous in measuring entanglement and Bell inequality violation. In this work, we show analytically that the basis that diagonalizes the spin-spin correlations is optimal for maximizing spin correlations, entanglement, and Bell inequality violation. We show that the optimal basis is approximately the same as the fixed beam basis (or the rotated beam basis) near the tt¯ production threshold, while it approaches the helicity basis far above threshold. Using this basis, we present the sensitivity for entanglement and Bell inequality violation in tt¯ events at the Large Hadron Collider (LHC) and a future e+e− collider. Since observing Bell inequality violation appears to be quite challenging experimentally, and requires a large dataset in collider experiments, choosing the optimal basis is crucially important to observe Bell inequality violation. Our method and general approach are equally applicable to other systems beyond tt¯, including interactions beyond the Standard Model. Published by the American Physical Society 2025