Observation of quantum entanglement in top-quark pairs using the ATLAS detector

We report the highest-energy observation of entanglement, in top$-$antitop quark events produced at the Large Hadron Collider, using a proton$-$proton collision data set with a center-of-mass energy of $\sqrt{s}=13$ TeV and an integrated luminosity of 140 fb$^{-1}$ recorded with the ATLAS experiment. Spin entanglement is detected from the measurement of a single observable $D$, inferred from the angle between the charged leptons in their parent top- and antitop-quark rest frames. The observable is measured in a narrow interval around the top$-$antitop quark production threshold, where the entanglement detection is expected to be significant. It is reported in a fiducial phase space defined with stable particles to minimize the uncertainties that stem from limitations of the Monte Carlo event generators and the parton shower model in modelling top-quark pair production. The entanglement marker 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 observed result is more than five standard deviations from a scenario without entanglement and hence constitutes both the first observation of entanglement in a pair of quarks and the highest-energy observation of entanglement to date.