Disentangling new physics with quantum entanglement in $t\bar{t}$ production at future lepton colliders

We investigate quantum entanglement and Bell-inequality violation in top-antitop pair production at future lepton colliders such as the International Linear Collider (ILC) and multi-TeV muon colliders. Within the Standard Model (SM), the process proceeds through $s$-channel $\gamma$ and $Z$ exchange and exhibits characteristic spin-correlation patterns that encode a non-trivial amount of entanglement. We then examine how these features are modified in several well-motivated extensions of the SM:(i) a neutral scalar mediator that couples to charged leptons and top quarks via Yukawa interactions and contributes as an additional $s$-channel exchange; (ii) the minimal gauged $U(1)_{B-L}$ model, which introduces a new neutral gauge boson $Z'$ coupling vectorially to SM fermions; and (iii) a Randall-Sundrum scenario, in which the exchange of massive Kaluza-Klein gravitons arising from a warped extra dimension induces additional spin-dependent interactions. For all cases, we evaluate quantum-information observables, including the entanglement marker, the concurrence, and the maximal Clauser-Horne-Shimony-Holt parameter, and study their dependence on the center-of-mass energy, scattering angle, and model parameters. We find that, relative to the SM expectation, the entanglement is typically reduced in the scalar-mediator scenario, while sizable deviations can arise in the $U(1)_{B-L}$ and Randall-Sundrum cases for phenomenologically relevant regions of parameter space. These results demonstrate the potential of quantum-information observables as sensitive probes of new neutral interactions and extra-dimensional dynamics in future lepton colliders.