Trace distance between density matrices: A nifty tool in new-physics searches

Quantum information methods have been brought to bear on high-energy physics, including the study of entanglement and Bell nonlocality in collider experiments. Quantum information observables have also been employed to constrain possible new-physics effects. We improve on this point by introducing quantum information tools routinely used to compare quantum states: the trace distance and the fidelity. We find that the former outperforms other quantum information observables considered in the literature and, together with the cross section, yields the strongest bounds on possible departures from the Standard Model. The power of the proposed methodology is demonstrated with three examples of new-physics searches. The first concerns the chromomagnetic dipole moment of the top quark and yields the first bound computed by means of quantum tomography and actual experimental data. The other two examples use Monte Carlo simulations and set the projected limits on the anomalous couplings of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>τ</a:mi></a:math> leptons at Belle and at a future collider—which is taken to be LEP3. For these new-physics searches, we also compare the sensitivity of the trace distance to those of other quantum information quantities like concurrence, magic, and the fidelity distance. In passing, we provide the first determinations of magic in collider data by analyzing the top-quark pair production at the LHC and the charmonium decays. The significance is well above the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>5</c:mn><c:mi>σ</c:mi></c:math> level in both the cases.