Entanglement and Bell Nonlocality in τ^+ τ^- at the LHC using Machine Learning for Neutrino Reconstruction

Experiments at the CERN Large Hadron Collider (LHC) have accumulated an unprecedented amount of data corresponding to a large variety of quantum states. Although searching for new particles beyond the Standard Model of particle physics remains a high priority for the LHC program, precision measurements of the physical processes predicted in the Standard Model continue to lead us to a deeper understanding of nature at high energies. We carry out detailed simulations for the process pp τ^+τ^- X to perform quantum tomography and to measure the quantum entanglement and the Bell nonlocality of the τ^+τ^- two qubit state, including both statistical and systematic uncertainties. By using advanced machine learning techniques for neutrino momentum reconstruction, we achieve precise measurements of the full spin density matrix, a critical advantage over previous studies limited by reconstruction challenges for missing momenta. Our analysis reveals a clear observation of Bell nonlocality with high statistical significance, surpassing 5σ, establishing τ^+ τ^- as an ideal system for quantum information studies in high-energy collisions. Given its experimental feasibility and the high expected sensitivity for Bell nonlocality, we propose that τ^+ τ^- should be regarded as the new benchmark system for quantum information studies at the LHC, complementing and extending the insights gained from the tt system.