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arXiv:2501.03311 · Physical review. D/Physical review. D.

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

M. Fabbrichesi, Matthew Low, Luca Marzola

Published Jun 19, 2025• 8 citations
arXivHTMLPDF

Abstract

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 τ 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 5 σ level in both the cases.

DOI
10.1103/kdmh-3yb4

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Abstract The measurement of quantum entanglement can provide a new and most sensitive probe to physics beyond the Standard Model. We use the concurrence of the top-quark pair spin states produced at colliders to constrain the magnetic dipole term in the coupling between top quark and gluons, that of τ\tau τ τ -lepton pair spin states to bound contact interactions and that of τ\tau τ τ -lepton pairs or two-photons spin states from the decay of the Higgs boson in trying to distinguish between CP-even and odd couplings. These four examples show the power of the new approach as well as its limitations. We show that differences in the entanglement in the top-quark and τ\tau τ τ -lepton pair production cross sections can provide constraints better than those previously estimated from total cross sections or classical correlations. Instead, the final states in the decays of the Higgs boson remain maximally entangled even in the presence of CP-odd couplings and cannot be used to set bounds on new physics. We discuss the violation of Bell inequalities featured in all four processes.
Recent studies have shown that quantitative concepts from quantum information theory can play a role in analyzing collider physics, including elucidating new physics. In this paper, we study various quantum information measures including , , and , in generic new physics scenarios modeled by the standard model effective field theory. We argue that such measures can indeed show up differences with respect to the pure standard model, and we compare our results with similar findings for the discussed previously in the literature. We examine the relative sensitivity of different measures to new physics in two-dimensional bins of the top pair invariant mass and scattering angle, finding that the concurrence, magic, and trace distance each emerge as the best measure in at least some regions of the phase space. This highlights the importance of exploring multiple quantum information measures in the hunt for beyond the standard model physics.
Measurements of top quark properties in CMS: ttˉt\bar{t}ttˉ spin density matrix, quantum entanglement and quantum magic
Polarization and spin correlation measurements of top quark-antiquark (ttˉt\bar{t}ttˉ) pairs provide tests of the standard model, but also new ways to test quantum mechanics with unstable particles at highest energies ever produced in a laboratory. Recent ttˉt\bar{t}ttˉ spin correlation measurements and the tests they enable, made with the CMS detector at the CERN LHC Run 2, are presented. The measurements summarized include the full spin density matrix measurement of top quark pairs using events with a single lepton and jets in the final state. Spin correlation measurements in specific phase space regions allow the observation of the entanglement phenomenon, and the measurement of quantum magic. From the measured spin correlation at the ttˉt\bar{t}ttˉ production threshold and high ttˉt\bar{t}ttˉ mass, entanglement is observed with a large fraction of the ttˉt\bar{t}ttˉ decays being spacelike separated. The observation of entanglement in ttˉt\bar{t}ttˉ events with two high transverse momentum leptons of opposite charge is also presented. Finally, the first TeV-scale experimental measurement of quantum magic, an important variable for the characterization of quantum states in quantum information science, is presented. These measurements provide one of the first connections between quantum information science and particle physics, and show the potential of collider experiments in the studies of the foundations of quantum mechanics.
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A bstract 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 5 σ , 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‾ t\overline{t} tt t t ¯ system.