Local vs. nonlocal entanglement in top-quark pairs at the LHC

We show that the entanglement observed in top-antitop quark spin states at the LHC is local in the energy region close to the production threshold. In contrast, nonlocal entanglement is observed in the central boosted region defined by a top-quark pair invariant mass $m_{t\bar{t}}>800$ GeV and scattering angles $\mathrm{\Theta }$ satisfying $\mathrm{\mid }\cos \mathrm{\Theta }\mathrm{\mid }<0.2$. This makes top-quark pairs a unique laboratory for studying the interplay between entanglement and Bell locality. The locality of entanglement near the production threshold is further supported by a recent CMS analysis, which reports a significance of more than $5\sigma$. We also demonstrate that there exists a kinematic region where the spin states of the top-antitop quark are separable, yet they exhibit non-zero discord and magic.