Observation of quantum entanglement in top-quark pair production using $pp$ collisions of $\sqrt{s} = 13$~\TeV\ with the ATLAS detector

We report the highest-energy observation of entanglement so far in top--antitop quark events produced at the Large Hadron Collider, using a proton$-$proton collision data set with a centre-of-mass energy of $\sqrt{s}=13$ TeV and an integrated luminosity of 140 fb$^{-1}$. Spin entanglement is detected from the measurement of a single observable $D$, inferred by the angle between the charged leptons in their parent top- and antitop-quark rest frames. The observable is measured on a narrow interval around the top-quark--antitop-quark production threshold, where the entanglement detection is expected to be significant. The entanglement observable is measured in a fiducial phase-space with stable particles. The entanglement witness is measured to be $D = -0.547 \pm 0.002~\text{(stat.)} \pm 0.021~\text{(syst.)}$ for $340 < m_{t\bar{t}} < 380$ GeV. The large spread in predictions from several mainstream event generators indicates that modelling this property is challenging. The predictions depend in particular on the parton-shower algorithm used. The observed result is more than five standard deviations from a scenario without entanglement and hence constitutes the first observation of entanglement in a pair of quarks, and the observation of entanglement at the highest energy to date.