Nonlocal advantage of quantum coherence in tau-lepton pairs from electron--positron collisions

Abstract

Quantum correlations have recently attracted significant attention in collider physics, with Nonlocal Advantage of Quantum Coherence (NAQC) representing the strongest form of quantum correlation studied so far. Owing to its strength, NAQC is considerably more challenging to observe than Bell nonlocality since it is only present in narrower regions of phase space. Unlike other systems, tau-lepton pair ($τ^+τ^-$) production in electron--positron ($e^+e^-$) collisions provides an ideal testing ground, as it exhibits strong quantum correlations and, in particular, NAQC over a large region of phase space. In this paper, we investigate NAQC in $e^+e^- \to τ^+τ^-$ production at center-of-mass energies of 10.58 and 91.19~GeV, corresponding to the ongoing Belle~II and future FCC-$ee$ experiments, respectively. Remarkably, for our experimental proposal, we develop a dedicated NAQC witness, which allows to certify NAQC presence by measuring one single magnitude. We estimate the experimental sensitivities needed to establish the presence of NAQC, finding that a large fraction of the number of events (specifically, 0.18 for Belle~II and 0.31 for FCC-$ee$) contribute to the NAQC signal. A 5$σ$ observation of NAQC requires a precision of approximately 1\% at Belle~II, while a precision of a few percent is sufficient at FCC-$ee$. The resulting observation would constitute the strongest form of quantum correlation measured in a collider to date. In addition, we design an experimental scheme to implement the steering game leading to the NAQC definition, representing the first implementation of a steering game in a high-energy collider. Our results are easily extendable to other electron--positron colliders with different center-of-mass energies.