Testing quantum entanglement and violation of the Bell inequality from the top-quark decay at the LHC

There is a significant interest in testing quantum entanglement and Bell inequality violation in high-energy experiments. Since the analyses in high-energy experiments are performed with events statistically averaged over phase space, the states used to determine observables depend on the choice of coordinates through an event-dependent basis and are thus not genuine quantum states, but rather “fictitious states”.

We find that the basis which diagonalizes the spin-spin correlations is optimal for constructing fictitious states to test the violation of Bell's inequality. This result is applied directly to the bipartite qubit system of a top and anti-top produced at a hadron collider. We propose searching for evidence of quantum entanglement in the semi-leptonic decay channel where the final state includes one lepton, one neutrino, two b-flavor tagged jets, and two light jets from the W decay. We find that this channel is both easier to reconstruct and has a larger effective quantity of data than the fully leptonic channel. As a result, the semi-leptonic channel is 60% more sensitive to quantum entanglement and a factor of 3 more sensitive to Bell inequality violation, compared to the leptonic channel.