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Spin versus nonstabilizerness in gluon and graviton scattering

John Gargalionis1,*, Nathan Moynihan2,†, Sokratis Trifinopoulos3,4,‡, Ewan N. V. Wallace1,§, Chris D. White2,∥, and Martin J. White1,¶

  • 1ARC Centre of Excellence for Dark Matter Particle Physics & CSSM, Department of Physics, University of Adelaide, Adelaide, SA 5005, Australia
  • 2Centre for Theoretical Physics, School of Physical and Chemical Sciences, Queen Mary University of London, 327 Mile End Road, London E1 4NS, United Kingdom
  • 3Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland
  • 4Physik-Institut, Universität Zürich, 8057 Zürich, Switzerland

  • *Contact author: john.gargalionis@adelaide.edu.au
  • †Contact author: n.moynihan@qmul.ac.uk
  • ‡Contact author: sokratis.trifinopoulos@cern.ch
  • §Contact author: ewan.n.wallace@adelaide.edu.au
  • ∥Contact author: christopher.white@qmul.ac.uk
  • Contact author: martin.white@adelaide.edu.au
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Phys. Rev. D 113, 016007 – Published 7 January, 2026

DOI: https://doi.org/10.1103/tcb9-3vpr

Abstract

The quantum property of nonstabilizerness, also known as magic, plays a key role in designing quantum computing systems. How to produce, manipulate, and enhance magic remains mysterious, such that concrete examples of physical systems that manifest magic behavior are sought after. In this paper, we study two-particle scattering of gluons and gravitons in Yang-Mills theory and general relativity, as well as their supersymmetric extensions. This provides an interesting case of two-qubit systems, differing only in the physical spin of the qubits. We show that magic is generically produced in both theories, and also show that magic typically decreases as the spin of the qubits increases. The maximal magic in each case is found to be substantially less than the known upper bound. Differences in the profile of magic generation can be traced to the known physics of each theory, as manifested in relations between their respective scattering amplitudes. Our case study may provide useful insights into understanding magic in other systems.

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Physics Subject Headings (PhySH)

Corrections

22 April, 2026

Correction: A project number in the fourth sentence of the Acknowledgments contained an error and has been fixed.

Article Text

References (124)

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2012).
  2. Y. Afik and J. R. M. n. de Nova, Entanglement and quantum tomography with top quarks at the LHC, Eur. Phys. J. Plus 136, 907 (2021).
  3. Z. Dong, D. Gonçalves, K. Kong, and A. Navarro, When the machine chimes the Bell: Entanglement and Bell inequalities with boosted tt¯, Phys. Rev. D 109, 115023 (2024).
  4. 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).
  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. C. Severi, C. D. E. Boschi, F. Maltoni, and M. Sioli, Quantum tops at the LHC: From entanglement to Bell inequalities, Eur. Phys. J. C 82, 285 (2022).
  7. Y. Afik and J. R. M. n. de Nova, Quantum information with top quarks in QCD, Quantum 6, 820 (2022).
  8. J. A. Aguilar-Saavedra and J. A. Casas, Improved tests of entanglement and Bell inequalities with LHC tops, Eur. Phys. J. C 82, 666 (2022).
  9. 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).
  10. 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).
  11. C. Severi and E. Vryonidou, Quantum entanglement and top spin correlations in SMEFT at higher orders, J. High Energy Phys. 01 (2023) 148.
  12. J. A. Aguilar-Saavedra, Postdecay quantum entanglement in top pair production, Phys. Rev. D 108, 076025 (2023).
  13. 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.
  14. E. L. Simpson, A new spin on top-quark physics: Using angular distributions to probe top-quark properties, and make the first observation of entanglement between quarks, Ph.D. thesis, Glasgow University, 2024.
  15. J. A. Aguilar-Saavedra, A closer look at post-decay tt¯ entanglement, Phys. Rev. D 109, 096027 (2024).
  16. F. Maltoni, C. Severi, S. Tentori, and E. Vryonidou, Quantum tops at circular lepton colliders, J. High Energy Phys. 09 (2024) 001.
  17. ATLAS Collaboration, Observation of quantum entanglement in top-quark pair production using pp collisions of s=13  TeV with the ATLAS detector, https://cds.cern.ch/record/2876054/files/ATLAS-CONF-2023-069.pdf.
  18. G. Aad et al. (ATLAS Collaboration), Observation of quantum entanglement in top-quark pairs using the ATLAS detector, Nature (London) 633, 542 (2024).
  19. 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).
  20. 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).
  21. S. A. Abel, M. Dittmar, and H. K. Dreiner, Testing locality at colliders via Bell’s inequality?, Phys. Lett. B 280, 304 (1992).
  22. S. A. Abel, H. K. Dreiner, R. Sengupta, and L. Ubaldi, Colliders are testing neither locality via Bell’s inequality nor entanglement versus non-entanglement, arXiv:2507.15949.
  23. P. Bechtle, C. Breuning, H. K. Dreiner, and C. Duhr, A critical appraisal of tests of locality and of entanglement versus non-entanglement at colliders, arXiv:2507.15947.
  24. M. Low, Addressing local realism through Bell tests at colliders, Phys. Rev. D 112, 096008 (2025).
  25. C. D. White and M. J. White, Magic states of top quarks, Phys. Rev. D 110, 116016 (2024).
  26. Q. Liu, I. Low, and Z. Yin, Maximal magic for two-qubit states, arXiv:2502.17550.
  27. Q. Liu, I. Low, and Z. Yin, Quantum magic in quantum electrodynamics, arXiv:2503.03098.
  28. M. Fabbrichesi, M. Low, and L. Marzola, The trace distance between density matrices, a nifty tool in new-physics searches, Phys. Rev. D 112, 013003 (2025).
  29. CMS Collaboration, Observation of magic states of top quark pairs produced in proton-proton collisions at s=13  TeV, https://cds.cern.ch/record/2926751/files/TOP-25-001-pas.pdf.
  30. Y. 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).
  31. R. Aoude, H. Banks, C. D. White, and M. J. White, Probing new physics in the top sector using quantum information, arXiv:2505.12522.
  32. A. J. Barr, P. Caban, and J. Rembieliński, Bell-type inequalities for systems of relativistic vector bosons, Quantum 7, 1070 (2023).
  33. R. Ashby-Pickering, A. J. Barr, and A. Wierzchucka, Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles, J. High Energy Phys. 05 (2023) 020.
  34. 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).
  35. J. A. Aguilar-Saavedra, Laboratory-frame tests of quantum entanglement in H→WW, Phys. Rev. D 107, 076016 (2023).
  36. F. Fabbri, J. Howarth, and T. Maurin, Isolating semi-leptonic H→WW* decays for Bell inequality tests, Eur. Phys. J. C 84, 20 (2024).
  37. R. Aoude, E. Madge, F. Maltoni, and L. Mantani, Probing new physics through entanglement in diboson production, J. High Energy Phys. 12 (2023) 017.
  38. M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Bell inequalities and quantum entanglement in weak gauge boson production at the LHC and future colliders, Eur. Phys. J. C 83, 823 (2023).
  39. K. Sakurai and M. Spannowsky, Three-body entanglement in particle decays, Phys. Rev. Lett. 132, 151602 (2024).
  40. C. Altomonte and A. J. Barr, Quantum state-channel duality for the calculation of Standard Model scattering amplitudes, Phys. Lett. B 847, 138303 (2023).
  41. Y. Afik, Y. Kats, J. R. M. n. de Nova, A. Soffer, and D. Uzan, Entanglement and Bell nonlocality with bottom-quark pairs at hadron colliders, Phys. Rev. D 111, L111902 (2025).
  42. J. A. Aguilar-Saavedra, Full quantum tomography of top quark decays, Phys. Lett. B 855, 138849 (2024).
  43. J. A. Aguilar-Saavedra, Tripartite entanglement in H→ZZ,WW decays, Phys. Rev. D 109, 113004 (2024).
  44. R. Grabarczyk, An improved Bell-CHSH observable for gauge boson pairs, arXiv:2410.18022.
  45. R. A. Morales, Tripartite entanglement and Bell non-locality in loop-induced Higgs boson decays, Eur. Phys. J. C 84, 581 (2024).
  46. C. Altomonte, A. J. Barr, M. Eckstein, P. Horodecki, and K. Sakurai, Prospects for quantum process tomography at high energies, Quantum Sci. Technol. 10, 045060 (2025).
  47. T. Han, M. Low, N. McGinnis, and S. Su, Measuring quantum discord at the LHC, J. High Energy Phys. 05 (2025) 081.
  48. K. Cheng, T. Han, and M. Low, Quantum tomography at colliders: With or without decays, Phys. Lett. B 868, 139675 (2025).
  49. A. Subba, R. K. Singh, and R. M. Godbole, Looking into the quantum entanglement in H→ZZ⋆ at LHC within SMEFT framework, arXiv:2411.19171.
  50. A. Subba and R. Rahaman, On bipartite and tripartite entanglement at present and future particle colliders, arXiv:2404.03292.
  51. P. Horodecki, K. Sakurai, A. S. Shaleena, and M. Spannowsky, Three-body non-locality in particle decays, J. High Energy Phys. 10 (2025) 160.
  52. M. Del Gratta, F. Fabbri, P. Lamba, F. Maltoni, and D. Pagani, Quantum properties of H→VV*: Precise predictions in the SM and sensitivity to new physics, J. High Energy Phys. 09 (2025) 013.
  53. P. Nason, E. Re, and L. Rottoli, Spin correlations in tt¯ production and decay at the LHC in QCD perturbation theory, J. High Energy Phys. 10 (2025) 149.
  54. M. Grossi, G. Pelliccioli, and A. Vicini, From angular coefficients to quantum observables: A phenomenological appraisal in di-boson systems, J. High Energy Phys. 12 (2024) 120.
  55. K. Cheng and B. Yan, Bell inequality violation of light quarks in back-to-back dihadron pair production at lepton colliders, Phys. Rev. Lett. 135, 011902 (2025).
  56. M. Ghodrati, String scattering amplitudes and mutual information in confining backgrounds: The partonic behavior, Phys. Rev. D 112, 046011 (2025).
  57. V. Balasubramanian, M. B. McDermott, and M. Van Raamsdonk, Momentum-space entanglement and renormalization in quantum field theory, Phys. Rev. D 86, 045014 (2012).
  58. S. Seki, I. Y. Park, and S.-J. Sin, Variation of entanglement entropy in scattering process, Phys. Lett. B 743, 147 (2015).
  59. R. Peschanski and S. Seki, Entanglement entropy of scattering particles, Phys. Lett. B 758, 89 (2016).
  60. G. Grignani and G. W. Semenoff, Scattering and momentum space entanglement, Phys. Lett. B 772, 699 (2017).
  61. D. E. Kharzeev and E. M. Levin, Deep inelastic scattering as a probe of entanglement, Phys. Rev. D 95, 114008 (2017).
  62. J. Fan, Y. Deng, and Y.-C. Huang, Variation of entanglement entropy and mutual information in fermion-fermion scattering, Phys. Rev. D 95, 065017 (2017).
  63. J. Fan and X. Li, Relativistic effect of entanglement in fermion-fermion scattering, Phys. Rev. D 97, 016011 (2018).
  64. A. Cervera-Lierta, J. I. Latorre, J. Rojo, and L. Rottoli, Maximal entanglement in high energy physics, SciPost Phys. 3, 036 (2017).
  65. S. R. Beane, D. B. Kaplan, N. Klco, and M. J. Savage, Entanglement suppression and emergent symmetries of strong interactions, Phys. Rev. Lett. 122, 102001 (2019).
  66. M. Rigobello, S. Notarnicola, G. Magnifico, and S. Montangero, Entanglement generation in (1+1)D QED scattering processes, Phys. Rev. D 104, 114501 (2021).
  67. I. Low and T. Mehen, Symmetry from entanglement suppression, Phys. Rev. D 104, 074014 (2021).
  68. Q. Liu, I. Low, and T. Mehen, Minimal entanglement and emergent symmetries in low-energy QCD, Phys. Rev. C 107, 025204 (2023).
  69. S. Fedida and A. Serafini, Tree-level entanglement in quantum electrodynamics, Phys. Rev. D 107, 116007 (2023).
  70. M. Blasone, S. De Siena, G. Lambiase, C. Matrella, and B. Micciola, Complete complementarity relations in tree level QED processes, Phys. Rev. D 111, 016007 (2025).
  71. C. Cheung, T. He, and A. Sivaramakrishnan, Entropy growth in perturbative scattering, Phys. Rev. D 108, 045013 (2023).
  72. M. Carena, I. Low, C. E. M. Wagner, and M.-L. Xiao, Entanglement suppression, enhanced symmetry, and a standard-model-like Higgs boson, Phys. Rev. D 109, L051901 (2024).
  73. R. Aoude, G. Elor, G. N. Remmen, and O. Sumensari, Positivity in amplitudes from quantum entanglement, arXiv:2402.16956.
  74. I. Low and Z. Yin, An area law for entanglement entropy in particle scattering, arXiv:2405.08056.
  75. I. Low and Z. Yin, Elastic cross section is entanglement entropy, Phys. Rev. D 111, 065027 (2025).
  76. J. Thaler and S. Trifinopoulos, Flavor patterns of fundamental particles from quantum entanglement?, Phys. Rev. D 111, 056021 (2025).
  77. N. McGinnis, Symmetry, entanglement, and the S-matrix, arXiv:2504.21079.
  78. M. Carena, G. Coloretti, W. Liu, M. Littmann, I. Low, and C. E. M. Wagner, Entanglement maximization and mirror symmetry in two-Higgs-doublet models, J. High Energy Phys. 08 (2025) 016.
  79. J. Liu, M. Tanaka, X.-P. Wang, J.-J. Zhang, and Z. Zheng, Scattering entanglement entropy and its implications for electroweak phase transitions, Phys. Rev. D 112, 015028 (2025).
  80. T.-R. Hu, K. Sone, F.-K. Guo, T. Hyodo, and I. Low, Entanglement suppression, quantum statistics and symmetries in spin-3/2 baryon scatterings, Phys. Rev. Res. 7, 043306 (2025).
  81. C. M. Sou, Y. Wang, and X. Zhang, Entanglement features in scattering mediated by heavy particles, J. High Energy Phys. 10 (2025) 003.
  82. M. Beverland, E. Campbell, M. Howard, and V. Kliuchnikov, Lower bounds on the non-clifford resources for quantum computations, Quantum Sci. Technol. 5, 035009 (2020).
  83. J. Jiang and X. Wang, Lower bound for the t count via unitary stabilizer nullity, Phys. Rev. Appl. 19, 034052 (2023).
  84. L. Leone, S. F. E. Oliviero, and A. Hamma, Learning t-doped stabilizer states, Quantum 8, 1361 (2024).
  85. H. Qassim, H. Pashayan, and D. Gosset, Improved upper bounds on the stabilizer rank of magic states, Quantum 5, 606 (2021).
  86. L. Leone, S. F. E. Oliviero, and A. Hamma, Stabilizer Rényi entropy, Phys. Rev. Lett. 128, 050402 (2022).
  87. T. Haug, S. Lee, and M. S. Kim, Efficient stabilizer entropies for quantum computers, Phys. Rev. Lett. 132, 240602 (2024).
  88. S. F. E. Oliviero, L. Leone, A. Hamma, and S. Lloyd, Measuring magic on a quantum processor, npj Quantum Inf. 8, 148 (2022).
  89. X. Turkeshi, M. Schirò, and P. Sierant, Measuring nonstabilizerness via multifractal flatness, Phys. Rev. A 108, 042408 (2023).
  90. A. Gu, L. Leone, S. Ghosh, J. Eisert, S. F. Yelin, and Y. Quek, Pseudomagic quantum states, Phys. Rev. Lett. 132, 210602 (2024).
  91. E. Tirrito, P. S. Tarabunga, G. Lami, T. Chanda, L. Leone, S. F. E. Oliviero, M. Dalmonte, M. Collura, and A. Hamma, Quantifying nonstabilizerness through entanglement spectrum flatness, Phys. Rev. A 109, L040401 (2024).
  92. X. Turkeshi, A. Dymarsky, and P. Sierant, Pauli spectrum and non-stabilizerness of typical quantum many-body states, Phys. Rev. B 111, 054301 (2025).
  93. L. Leone and L. Bittel, Stabilizer entropies are monotones for magic-state resource theory, Phys. Rev. A 110, L040403 (2024).
  94. P. S. Tarabunga, E. Tirrito, T. Chanda, and M. Dalmonte, Many-body magic via Pauli-Markov Chains—from criticality to gauge theories, PRX Quantum 4, 040317 (2023).
  95. M. Frau, P. S. Tarabunga, M. Collura, M. Dalmonte, and E. Tirrito, Nonstabilizerness versus entanglement in matrix product states, Phys. Rev. B 110, 045101 (2024).
  96. G. Lami, T. Haug, and J. De Nardis, Quantum state designs with Clifford enhanced matrix product states, PRX Quantum 6, 010345 (2025).
  97. C. E. P. Robin and M. J. Savage, Quantum complexity fluctuations from nuclear and hypernuclear forces, Phys. Rev. C 112, 044004 (2025).
  98. I. Chernyshev, C. E. P. Robin, and M. J. Savage, Quantum magic and computational complexity in the neutrino sector, Phys. Rev. Res. 7, 023228 (2025).
  99. G. Busoni, J. Gargalionis, E. N. V. Wallace, and M. J. White, Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabilizerness, Phys. Rev. D 112, 035022 (2025).
  100. H. Kawai, D. C. Lewellen, and S. H. H. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B269, 1 (1986).
  101. Z. Bern, J. J. M. Carrasco, and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78, 085011 (2008).
  102. Z. Bern, J. J. M. Carrasco, and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105, 061602 (2010).
  103. Z. Bern, J. J. Carrasco, W.-M. Chen, H. Johansson, and R. Roiban, Gravity amplitudes as generalized double copies of gauge-theory amplitudes, Phys. Rev. Lett. 118, 181602 (2017).
  104. Z. Bern, T. Dennen, Y.-t. Huang, and M. Kiermaier, Gravity as the square of gauge theory, Phys. Rev. D 82, 065003 (2010).
  105. R. Monteiro, D. O’Connell, and C. D. White, Black holes and the double copy, J. High Energy Phys. 12 (2014) 056.
  106. A. Luna, R. Monteiro, I. Nicholson, and D. O’Connell, Type D spacetimes and the Weyl double copy, Classical Quantum Gravity 36, 065003 (2019).
  107. C. D. White, Twistorial foundation for the classical double copy, Phys. Rev. Lett. 126, 061602 (2021).
  108. E. Chacón, S. Nagy, and C. D. White, The Weyl double copy from twistor space, J. High Energy Phys. 05 (2021) 2239.
  109. W. D. Goldberger and A. K. Ridgway, Radiation and the classical double copy for color charges, Phys. Rev. D 95, 125010 (2017).
  110. A. Anastasiou, L. Borsten, M. J. Duff, S. Nagy, and M. Zoccali, Gravity as gauge theory squared: A ghost story, Phys. Rev. Lett. 121, 211601 (2018).
  111. Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, The duality between color and kinematics and its applications, J. Phys. A 57, 333002 (2024).
  112. T. Adamo, J. J. M. Carrasco, M. Carrillo-González, M. Chiodaroli, H. Elvang, H. Johansson, D. O’Connell, R. Roiban, and O. Schlotterer, Snowmass white paper: The double copy and its applications, in Snowmass 2021 (2022), arXiv:2204.06547.
  113. C. D. White, The Classical Double Copy (World Scientific, Singapore, 2024).
  114. K. Kowalska and E. M. Sessolo, Entanglement in flavored scalar scattering, J. High Energy Phys. 07 (2024) 156.
  115. C. Núñez, A. Cervera-Lierta, and J. I. Latorre, Universality of entanglement in gluon dynamics, arXiv:2504.15353.
  116. H. Elvang and Y.-t. Huang, Scattering Amplitudes in Gauge Theory and Gravity (Cambridge University Press, Cambridge, England, 2015).
  117. J. M. Henn and J. C. Plefka, Scattering Amplitudes in Gauge Theories (Springer, Berlin, 2014), Vol. 883.
  118. M. D. Schwartz, Quantum Field Theory and the Standard Model (Cambridge University Press, Cambridge, England, 2014).
  119. S. J. Parke and T. R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56, 2459 (1986).
  120. V. Del Duca, L. J. Dixon, and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys. B571, 51 (2000).
  121. M. T. Grisaru and H. N. Pendleton, Some properties of scattering amplitudes in supersymmetric theories, Nucl. Phys. B124, 81 (1977).
  122. M. Bianchi, H. Elvang, and D. Z. Freedman, Generating tree amplitudes in N=4 SYM and N=8 SG, J. High Energy Phys. 09 (2008) 063.
  123. L. J. Dixon, J. M. Henn, J. Plefka, and T. Schuster, All tree-level amplitudes in massless QCD, J. High Energy Phys. 01 (2011) 035.
  124. M. T. Grisaru, H. N. Pendleton, and P. van Nieuwenhuizen, Supergravity and the S matrix, Phys. Rev. D 15, 996 (1977).

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Phys. Rev. D 113, 016007– Published 7 January, 2026
  • Received 1 October 2025
  • Accepted 5 December 2025
  • Corrected 22 April 2026
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