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Probing quantum entanglement with generalized parton distributions at the Electron-Ion Collider

Yoshitaka Hatta1,2 and Jakob Schoenleber1,2

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Phys. Rev. D 113, 094016 – Published 8 May, 2026

DOI: https://doi.org/10.1103/qdb2-k2nh

Abstract

Within the collinear factorization framework based on generalized parton distributions, we calculate the spin density matrix of exclusively produced quark and antiquark pairs uu¯, dd¯, ss¯, cc¯, bb¯ in electron-proton scattering. The presence of both real and imaginary parts in the scattering amplitudes leads to a rich pattern of entanglement between the quark and the antiquark. We map out kinematical regions where the pairs exhibit entanglement, Bell nonlocality, and nonstabilizerness. We also predict that massive quarks and antiquarks are transversely polarized, similar to the well-known transverse hyperon polarization in unpolarized collisions. In strangeness, charm, and bottom productions, the polarization can reach 50%–80% in certain kinematic regions in the low-energy runs of the Electron-Ion Collider.

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References (75)

  1. C. S. Wu and I. Shaknov, The angular correlation of scattered annihilation radiation, Phys. Rev. 77, 136 (1950).
  2. J. S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics (Long Island City, N.Y.) 1, 195 (1964).
  3. John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt, Proposed experiment to test local hidden variable theories, Phys. Rev. Lett. 23, 880 (1969).
  4. Alain Aspect, Philippe Grangier, and Gerard Roger, Experimental tests of realistic local theories via Bell’s theorem, Phys. Rev. Lett. 47, 460 (1981).
  5. Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, and Anton Zeilinger, Violation of Bell’s inequality under strict Einstein locality conditions, Phys. Rev. Lett. 81, 5039 (1998).
  6. Werner Bernreuther and Arnd Brandenburg, Tracing CP violation in the production of top quark pairs by multiple TeV proton proton collisions, Phys. Rev. D 49, 4481 (1994).
  7. Matthew Baumgart and Brock Tweedie, A new twist on top quark spin correlations, J. High Energy Phys. 03 (2013) 117.
  8. Werner Bernreuther, Dennis Heisler, and Zong-Guo Si, A set of top quark spin correlation and polarization observables for the LHC: Standard Model predictions and new physics contributions, J. High Energy Phys. 12 (2015) 026.
  9. Yoav Afik and Juan Ramón Muñoz de Nova, Entanglement and quantum tomography with top quarks at the LHC, Eur. Phys. J. Plus 136, 907 (2021).
  10. Zhongtian Dong, Dorival Gonçalves, Kyoungchul Kong, and Alberto Navarro, Entanglement and Bell inequalities with boosted tt¯, Phys. Rev. D 109, 115023 (2024).
  11. Georges Aad et al., Observation of quantum entanglement with top quarks at the ATLAS detector, Nature (London) 633, 542 (2024).
  12. Aram Hayrapetyan et al., Observation of quantum entanglement in top quark pair production in proton–proton collisions at s=13  TeV, Rep. Prog. Phys. 87, 117801 (2024).
  13. Aram Hayrapetyan et al., 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. Albert M. Sirunyan et al., 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).
  15. Alan J. Barr, Marco Fabbrichesi, Roberto Floreanini, Emidio Gabrielli, and Luca Marzola, Quantum entanglement and Bell inequality violation at colliders, Prog. Part. Nucl. Phys. 139, 104134 (2024).
  16. Yoav Afik et al., Quantum information meets high-energy physics: Input to the update of the European strategy for particle physics, Eur. Phys. J. Plus 140, 855 (2025).
  17. J. A. Aguilar-Saavedra, Laboratory-frame tests of quantum entanglement in H→WW, Phys. Rev. D 107, 076016 (2023).
  18. Marco Fabbrichesi, Roberto Floreanini, Emidio Gabrielli, and Luca Marzola, Bell inequalities and quantum entanglement in weak gauge boson production at the LHC and future colliders, Eur. Phys. J. C 83, 823 (2023).
  19. Mohammad Mahdi Altakach, Priyanka Lamba, Fabio Maltoni, Kentarou Mawatari, and Kazuki Sakurai, Quantum information and CP measurement in H→τ+τ- at future lepton colliders, Phys. Rev. D 107, 093002 (2023).
  20. Tao Han, Matthew Low, and Youle Su, Entanglement and Bell nonlocality in τ+τ− at the BEPC, J. High Energy Phys. 10 (2025) 217.
  21. Yevgeny Kats and David Uzan, Prospects for measuring quark polarization and spin correlations in bb¯ and cc¯ samples at the LHC, J. High Energy Phys. 03 (2024) 063.
  22. Yoav Afik, Yevgeny Kats, Juan Ramón Muñoz de Nova, Abner Soffer, and David Uzan, Entanglement and Bell nonlocality with bottom-quark pairs at hadron colliders, Phys. Rev. D 111, L111902 (2025).
  23. Kun Cheng and Bin Yan, Bell inequality violation of light quarks in dihadron pair production at lepton colliders, Phys. Rev. Lett. 135, 011902 (2025).
  24. M. Fabbrichesi, R. Floreanini, and G. Panizzo, Testing Bell inequalities at the LHC with top-quark pairs, Phys. Rev. Lett. 127, 161801 (2021).
  25. Claudio Severi, Cristian Degli Esposti Boschi, Fabio Maltoni, and Maximiliano Sioli, Quantum tops at the LHC: From entanglement to Bell inequalities, Eur. Phys. J. C 82, 285 (2022).
  26. S. A. Abel, M. Dittmar, and Herbert K. Dreiner, Testing locality at colliders via Bell’s inequality?, Phys. Lett. B 280, 304 (1992).
  27. Steven A. Abel, Herbi K. Dreiner, Rhitaja Sengupta, and Lorenzo Ubaldi, Colliders are Testing neither locality via Bell’s inequality nor entanglement versus non-entanglement, arXiv:2507.15949.
  28. Matthew Low, Addressing local realism through Bell tests at colliders, Phys. Rev. D 112, 096008 (2025).
  29. Wei Qi, Zijing Guo, and Bo-Wen Xiao, Studying maximal entanglement and Bell nonlocality at an electron-ion collider, Phys. Rev. D 113, 054048 (2026).
  30. Michael Fucilla and Yoshitaka Hatta, Spin-spin entanglement in diffractive heavy-quark production, Phys. Rev. D 113, L031504 (2026).
  31. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider: EIC yellow report, Nucl. Phys. A1026, 122447 (2022).
  32. M. Diehl, Generalized parton distributions, Phys. Rep. 388, 41 (2003).
  33. A. V. Belitsky and A. V. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rep. 418, 1 (2005).
  34. Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, Stabilizer Rényi entropy, Phys. Rev. Lett. 128, 050402 (2022).
  35. Chris D. White and Martin J. White, Magic states of top quarks, Phys. Rev. D 110, 116016 (2024).
  36. G. Bunce et al., Lambda0 hyperon polarization in inclusive production by 300-GeV protons on beryllium, Phys. Rev. Lett. 36, 1113 (1976).
  37. B. Lundberg et al., Polarization in inclusive Λ and Λ¯ production at large pT, Phys. Rev. D 40, 3557 (1989).
  38. A. Airapetian et al., Transverse polarization of Λ and Λ¯ hyperons in quasireal photoproduction, Phys. Rev. D 76, 092008 (2007).
  39. M. G. Alexeev et al., Probing transversity by measuring Λ polarisation in SIDIS, Phys. Lett. B 824, 136834 (2022).
  40. V. M. Braun and D. Yu. Ivanov, Exclusive diffractive electroproduction of dijets in collinear factorization, Phys. Rev. D 72, 034016 (2005).
  41. John David Jackson, Classical Electrodynamics (Wiley, New York, 1998).
  42. Asher Peres and Daniel R. Terno, Quantum information and relativity theory, Rev. Mod. Phys. 76, 93 (2004).
  43. M. Jacob and G. C. Wick, On the general theory of collisions for particles with spin, Ann. Phys. (N.Y.) 7, 404 (1959).
  44. Michael E. Peskin and Daniel V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, MA, 1995).
  45. Kun Cheng, Tao Han, and Sokratis Trifinopoulos, Quantum information at the electron-ion collider, arXiv:2510.23773.
  46. Zuo-tang Liang and C. Boros, Hyperon polarization and single spin left-right asymmetry in inclusive production processes at high-energies, Phys. Rev. Lett. 79, 3608 (1997).
  47. Y. Kanazawa and Yuji Koike, Polarization in hadronic Lambda hyperon production and chiral odd twist—three quark distribution, Phys. Rev. D 64, 034019 (2001).
  48. M. Anselmino, Daniel Boer, U. D’Alesio, and F. Murgia, Transverse lambda polarization in semiinclusive DIS, Phys. Rev. D 65, 114014 (2002).
  49. Jian Zhou, Feng Yuan, and Zuo-Tang Liang, Hyperon polarization in unpolarized scattering processes, Phys. Rev. D 78, 114008 (2008).
  50. Yuji Koike, Andreas Metz, Daniel Pitonyak, Kenta Yabe, and Shinsuke Yoshida, Twist-3 fragmentation contribution to polarized hyperon production in unpolarized hadronic collisions, Phys. Rev. D 95, 114013 (2017).
  51. Zhong-Bo Kang, John Terry, Anselm Vossen, Qinghua Xu, and Jinlong Zhang, Transverse Lambda production at the future electron-ion collider, Phys. Rev. D 105, 094033 (2022).
  52. Welathantri G. D. Dharmaratna and Gary R. Goldstein, Single quark polarization in quantum chromodynamics subprocesses, Phys. Rev. D 53, 1073 (1996).
  53. Sanjin Benić, Yoshitaka Hatta, Abhiram Kaushik, and Hsiang-nan Li, Perturbative QCD contribution to transverse single spin asymmetries in the Drell-Yan process and SIDIS, Phys. Rev. D 109, 074038 (2024).
  54. Yoshitaka Hatta, Bo-Wen Xiao, and Feng Yuan, Gluon tomography from deeply virtual Compton scattering at small-x, Phys. Rev. D 95, 114026 (2017).
  55. Nikolai N. Nikolaev and B. G. Zakharov, Splitting the Pomeron into two jets: A novel process at HERA, Phys. Lett. B 332, 177 (1994).
  56. Jochen Bartels, H. Lotter, and M. Wüsthoff, Quark-antiquark production in DIS diffractive dissociation, Phys. Lett. B 379, 239 (1996); 382, 449 (1996).
  57. Asher Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77, 1413 (1996).
  58. Pawel Horodecki, Separability criterion and inseparable mixed states with positive partial transposition, Phys. Lett. A 232, 333 (1997).
  59. Matthias D. Lang and Carlton M. Caves, Quantum discord and the geometry of Bell-Diagonal states, Phys. Rev. Lett. 105, 150501 (2010).
  60. R. Horodecki, P. Horodecki, and M. Horodecki, Violating Bell inequality by mixed spin- 1 2 states: Necessary and sufficient condition, Phys. Lett. A 200, 340 (1995).
  61. Reinhard F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40, 4277 (1989).
  62. Daniel Gottesman, The Heisenberg representation of quantum computers, in Proceedings of the 22nd International Colloquium on Group Theoretical Methods in Physics (International Press, 1998), pp. 32–43.
  63. Qiaofeng Liu, Ian Low, and Zhewei Yin, Quantum magic in quantum electrodynamics, Phys. Rev. D 113, 056001 (2026).
  64. John Gargalionis, Nathan Moynihan, Sokratis Trifinopoulos, Ewan N. V. Wallace, Chris D. White, and Martin J. White, Spin versus nonstabilizerness in gluon and graviton scattering, Phys. Rev. D 113, 016007 (2026).
  65. Qiaofeng Liu, Ian Low, and Zhewei Yin, Maximal magic for two-qubit states, Quantum Sci. Technol. 11, 015035 (2026).
  66. S. V. Goloskokov and P. Kroll, The Longitudinal cross-section of vector meson electroproduction, Eur. Phys. J. C 50, 829 (2007).
  67. S. V. Goloskokov and P. Kroll, The Role of the quark and gluon GPDs in hard vector-meson electroproduction, Eur. Phys. J. C 53, 367 (2008).
  68. Yoshitaka Hatta, Henry T. Klest, Kornelija Passek-K., and Jakob Schoenleber, Deeply virtual ϕ-meson production near threshold, arXiv:2501.12343.
  69. Henry T. Klest, Studying two-photon exchange in deep inelastic scattering with HERA data, Phys. Rev. D 113, 014045 (2026).
  70. Mario Galanti, Andrea Giammanco, Yuval Grossman, Yevgeny Kats, Emmanuel Stamou, and Jure Zupan, Heavy baryons as polarimeters at colliders, J. High Energy Phys. 11 (2015) 067.
  71. Francois Gelis, Edmond Iancu, Jamal Jalilian-Marian, and Raju Venugopalan, The color glass condensate, Annu. Rev. Nucl. Part. Sci. 60, 463 (2010).
  72. R. Boussarie, A. V. Grabovsky, L. Szymanowski, and S. Wallon, On the one loop γ(*)→qq¯ impact factor and the exclusive diffractive cross sections for the production of two or three jets, J. High Energy Phys. 11 (2016) 149.
  73. Nils A. Tornqvist, Suggestion for Einstein-Podolsky-Rosen experiments using reactions like e+e−→ΛΛ¯→π−pπ+p¯, Found. Phys. 11, 171 (1981).
  74. Shi-Jia Lin, Ming-Jun Liu, Ding Yu Shao, and Shu-Yi Wei, Spin correlations and Bell nonlocality in ΛΛ¯ pair production from e+e− collisions with a thrust cut, J. High Energy Phys. 11 (2025) 082.
  75. Jiayin Gu, Shi-Jia Lin, Ding Yu Shao, Lian-Tao Wang, and Si-Xiang Yang, Decoherence in high energy collisions as renormalization group flow, arXiv:2510.13951.

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Phys. Rev. D 113, 094016– Published 8 May, 2026
  • Received 26 November 2025
  • Accepted 22 April 2026
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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.

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