- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

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

M. Fabbrichesi1, M. Low2, and L. Marzola3,4

  • 1INFN, Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy
  • 2Pittsburgh Particle Physics, Astrophysics, and Cosmology Center, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA
  • 3Laboratory of High-Energy and Computational Physics, NICPB, Rävala pst 10, 10143 Tallinn, Estonia
  • 4Institute of Computer Science, University of Tartu, Narva mnt 18, 51009 Tartu, Estonia

PDF

Phys. Rev. D 112, 013003 – Published 7 July, 2025

DOI: https://doi.org/10.1103/kdmh-3yb4

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 5σ level in both the cases.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. A. J. Barr, M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Quantum entanglement and Bell inequality violation at colliders, Prog. Part. Nucl. Phys. 139, 104134 (2024).
  2. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  3. Y. Afik and J. R. M. de Nova, Entanglement and quantum tomography with top quarks at the LHC, Eur. Phys. J. Plus 136, 907 (2021).
  4. J. Bell, On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz. 1, 195 (1964).
  5. M. Fabbrichesi, R. Floreanini, and G. Panizzo, Testing Bell inequalities at the LHC with top-quark pairs, Phys. Rev. Lett. 127, 161801 (2021).
  6. A. J. Barr, Testing Bell inequalities in Higgs boson decays, Phys. Lett. B 825, 136866 (2022).
  7. J. A. Aguilar-Saavedra, A. Bernal, J. A. Casas, and J. M. Moreno, Testing entanglement and Bell inequalities in H→ZZ, Phys. Rev. D 107, 016012 (2023).
  8. K. Ehatäht, M. Fabbrichesi, L. Marzola, and C. Veelken, Probing entanglement and testing Bell inequality violation with e+e→τ+τ− at Belle II, Phys. Rev. D 109, 032005 (2024).
  9. M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Bell inequality is violated in B0→J/ψK*(892)0 decays, Phys. Rev. D 109, L031104 (2024).
  10. M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Bell inequality is violated in charmonium decays, Phys. Rev. D 110, 053008 (2024).
  11. G. Aad et al. (ATLAS Collaboration), Observation of quantum entanglement in top-quark pairs using the ATLAS detector, Nature (London) 633, 542 (2024).
  12. CMS Collaboration, Observation of quantum entanglement in top quark pair production in proton–proton collisions at s=13  TeV, Rep. Prog. Phys. 87, 117801 (2024).
  13. A. Hayrapetyan et al. (CMS Collaboration), Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using lepton+jets events from proton-proton collisions at s=13  TeV, Phys. Rev. D 110, 112016 (2024).
  14. R. Aoude, E. Madge, F. Maltoni, and L. Mantani, Quantum SMEFT tomography: Top quark pair production at the LHC, Phys. Rev. D 106, 055007 (2022).
  15. M. Fabbrichesi, R. Floreanini, and E. Gabrielli, Constraining new physics in entangled two-qubit systems: Top-quark, tau-lepton and photon pairs, Eur. Phys. J. C 83, 162 (2023).
  16. F. Maltoni, C. Severi, S. Tentori, and E. Vryonidou, Quantum detection of new physics in top-quark pair production at the LHC, J. High Energy Phys. 03 (2024) 099.
  17. M. M. Altakach, P. Lamba, F. Maltoni, K. Mawatari, and K. Sakurai, Quantum information and CP measurement in H→τ+τ- at future lepton colliders, Phys. Rev. D 107, 093002 (2023).
  18. M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Stringent bounds on HWW and HZZ anomalous couplings with quantum tomography at the LHC, J. High Energy Phys. 09 (2023) 195.
  19. A. Bernal, P. Caban, and J. Rembieliński, Entanglement and Bell inequalities violation in H→ZZ with anomalous coupling, Eur. Phys. J. C 83, 1050 (2023).
  20. R. Aoude, E. Madge, F. Maltoni, and L. Mantani, Probing new physics through entanglement in diboson production, J. High Energy Phys. 12 (2023) 017.
  21. M. Fabbrichesi and L. Marzola, Dipole momenta and compositeness of the τ lepton at Belle II, Phys. Rev. D 109, 095026 (2024).
  22. M. Fabbrichesi and L. Marzola, Quantum tomography with τ leptons at the FCC-ee: Entanglement, Bell inequality violation, sinθW, and anomalous couplings, Phys. Rev. D 110, 076004 (2024).
  23. Y. Afik and J. R. M. n. de Nova, Quantum discord and steering in top quarks at the LHC, Phys. Rev. Lett. 130, 221801 (2023).
  24. C. D. White and M. J. White, The magic of entangled top quarks, Phys. Rev. D 110, 116016 (2024).
  25. T. Han, M. Low, N. McGinnis, and S. Su, Measuring quantum discord at the LHC, J. High Energy Phys. 05 (2025) 081.
  26. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2012), p. 6.
  27. A. Uhlmann, The “transition probability” in the state space of a *-algebra, Rep. Math. Phys. 9, 273 (1976).
  28. C. A. Fuchs and J. van de Graaf, Cryptographic distinguishability measures for quantum-mechanical states, IEEE Trans. Inf. Theory 45, 1216 (1999).
  29. A. Gilchrist, N. K. Langford, and M. A. Nielsen, Distance measures to compare real and ideal quantum processes, Phys. Rev. A 71, 062310 (2005).
  30. Albert M. Sirunyan et al. (CMS Collaboration), Measurement of the top quark polarization and tt¯ spin correlations using dilepton final states in proton-proton collisions at s=13  TeV, Phys. Rev. D 100, 072002 (2019).
  31. R. D. Ball et al. (PDF4LHC Working Group Collaboration), The PDF4LHC21 combination of global PDF fits for the LHC Run III, J. Phys. G 49, 080501 (2022).
  32. C. Severi and E. Vryonidou, Quantum entanglement and top spin correlations in SMEFT at higher orders, J. High Energy Phys. 01 (2023) 148.
  33. M. Fabbrichesi, M. Pinamonti, and A. Tonero, Stringent limits on top-quark compositeness from tt¯ production at the Tevatron and the LHC, Phys. Rev. D 89, 074028 (2014).
  34. I. Brivio, S. Bruggisser, F. Maltoni, R. Moutafis, T. Plehn, E. Vryonidou, S. Westhoff, and C. Zhang, O new physics, where art thou? A global search in the top sector, J. High Energy Phys. 02 (2020) 131.
  35. DELPHI Collaboration, Study of tau-pair production in photon-photon collisions at LEP and limits on the anomalous electromagnetic moments of the tau lepton, Eur. Phys. J. C 35, 159 (2004).
  36. S. Eidelman and M. Passera, Theory of the τ lepton anomalous magnetic moment, Mod. Phys. Lett. A 22, 159 (2007).
  37. K. Inami et al. (Belle Collaboration), An improved search for the electric dipole moment of the τ lepton, J. High Energy Phys. 04 (2022) 110.
  38. A. Crivellin, M. Hoferichter, and J. M. Roney, Toward testing the magnetic moment of the tau at one part per million, Phys. Rev. D 106, 093007 (2022).
  39. J. Bernabeu, G. A. Gonzalez-Sprinberg, and J. Vidal, Tau spin correlations and the anomalous magnetic moment, J. High Energy Phys. 01 (2009) 062.
  40. J. Bernabéu, G. González-Sprinberg, J. Papavassiliou, and J. Vidal, Tau anomalous magnetic moment form factor at super b/flavor factories, Nucl. Phys. B790, 160 (2008).
  41. X. Chen and Y. Wu, Search for the electric dipole moment and anomalous magnetic moment of the tau lepton at tau factories, J. High Energy Phys. 10 (2019) 089.
  42. W. Bernreuther, L. Chen, and O. Nachtmann, Electric dipole moment of the tau lepton revisited, Phys. Rev. D 103, 096011 (2021).
  43. S. Banerjee, B. Pietrzyk, J. M. Roney, and Z. Was, Tau and muon pair production cross-sections in electron-positron annihilations at s=10.58 GeV, Phys. Rev. D 77, 054012 (2008).
  44. R. L. Workman et al. (Particle Data Group Collaboration), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  45. M. Jacob and G. C. Wick, On the general theory of collisions for particles with spin, Ann. Phys. (N.Y.) 7, 404 (1959).
  46. E. Leader, Spin in Particle Physics, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology Vol. 15 (Cambridge University Press, Cambridge, England, 2023).
  47. K. Cheng, T. Han, and M. Low, Quantum tomography at colliders: With or without decays, arXiv:2410.08303.
  48. B. Grzadkowski, M. Iskrzyński, M. Misiak, and J. Rosiek, Dimension-six terms in the standard model lagrangian, J. High Energy Phys. 10 (2010) 085.
  49. A. Blondel et al., LEP3: A high luminosity e+e− collider to study the Higgs boson, arXiv:1208.0504.
  50. W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
  51. S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A 70, 052328 (2004).
  52. T. Han, M. Low, and T. A. Wu, Quantum entanglement and Bell inequality violation in semi-leptonic top decays, J. High Energy Phys. 07 (2024) 192.
  53. K. Cheng, T. Han, and M. Low, Optimizing fictitious states for Bell inequality violation in bipartite qubit systems with applications to the tt− system, Phys. Rev. D 109, 116005 (2024).
  54. K. Cheng, T. Han, and M. Low, Optimizing entanglement and Bell inequality violation in top anti-top events, Phys. Rev. D 111, 033004 (2025).
  55. M. Ablikim et al. (BESIII Collaboration), Number of J/ψ events at BESIII, Chin. Phys. C 46, 074001 (2022).
  56. M. Ablikim et al. (BESIII Collaboration), Precise measurements of decay parameters and CP asymmetry with entangled Λ−Λ¯ pairs, Phys. Rev. Lett. 129, 131801 (2022).

Outline

Information

Phys. Rev. D 112, 013003– Published 7 July, 2025
  • Received 21 January 2025
  • Accepted 19 June 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation