Experimental characterization of the hierarchy of quantum correlations in top quark pairs

Abstract: Recent results from the Large Hadron Collider have demonstrated quantum entanglement of top quark-antiquark pairs using the spin degree of freedom. Based on the doubly differential measurement of the spin density matrix of the top quark and antiquark performed by the CMS collaboration in the helicity and beam bases, we evaluate a set of quantum observables, including discord, steering, Bell correlation, and magic. These observables allow for a quantitative characterization of the quantum correlations present in a top quark--antiquark system, thus enabling an interpretation of collider data in terms of quantum states and their properties. Discord is observed to be greater than zero with a significance of more than 5 standard deviations ($σ$). Evidence for steering is found with a significance of more than 3$σ$. This is the first evidence for steering, and the first observation of discord in a high-energy system. No Bell correlation is observed within the currently probed phase space, in agreement with the theoretical prediction. These results experimentally corroborate the full hierarchy of quantum correlations in top quarks with discord being the most basic form of quantum correlation, followed by entanglement, steering and Bell correlation. The significance of nonzero magic, which is a complementary observable to the quantum-correlation hierarchy, is found to exceed 5$σ$ in several regions of phase space.