- Open Access
Tests of quantum contextuality in particle physics
Phys. Rev. D 112, 033005 – Published 19 August, 2025
DOI: https://doi.org/10.1103/22zl-ltxm
Abstract
Quantum contextuality refers to the impossibility of assigning a predefined, intrinsic value to a physical property of a system independently of the context in which the property is measured. It is, perhaps, the most fundamental feature of quantum mechanics. The many states with different spin that particle physics provides are the ideal setting for testing contextuality. We verify that the polarization states of single spin-1 massive particles produced at colliders are contextual. We test gauge bosons produced in top-quark decays, and mesons in -meson decays and mesons in and charmonium decays by reinterpreting the data and the analyses of the ATLAS, LHCb, Belle II and BESIII experimental collaborations, respectively. The polarization states of these four particles show contextuality with a significance larger than . We also discuss the presence of quantum contextuality in spin states of bipartite systems formed by spin- particles. We test and baryons reinterpreting two BESIII data analyses, and pairs of top quarks utilizing a recent analysis of the CMS Collaboration. Quantum contextuality is present with a significance exceeding also in these cases. In addition, we study the feasibility of testing quantum contextuality by means of boson production in association with the Higgs boson, and bosons pairs created in Higgs boson decays and with pairs of leptons. For the latter, we use Monte Carlo simulations that mimic the settings of SuperKEKB and of future lepton colliders. Experiments at high energies, though not designed for the purpose, perform surprisingly well in testing for quantum contextuality.
Physics Subject Headings (PhySH)
Article Text
References (82)
- 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).
- R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
- F. Benatti, M. Fannes, R. Floreanini, and D. Petritis, Quantum Information, Computation and Cryptography (Springer, Berlin, Heidelberg, 2010).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2012).
- D. Bruss and G. Leuchs, Quantum Information: From Foundations to Quantum Technology Applications (Wiley, New York, 2019).
- J. Bell, On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz. 1, 195 (1964).
- V. Scarani, Bell Nonlocality (Oxford University Press, New York, 2019).
- J. S. Bell, On the problem of hidden variables in quantum mechanics, Rev. Mod. Phys. 38, 447 (1966).
- S. Kochen and E. Specker, The problem of hidden variables in quantum mechanics, J. Math. Mech. 17, 59 (1968).
- M. Michler, H. Weinfurter, and M. Żukowski, Experiments towards falsification of noncontextual hidden variable theories, Phys. Rev. Lett. 84, 5457 (2000).
- Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, Experimental test of the Kochen-Specker theorem with single photons, Phys. Rev. Lett. 90, 250401 (2003).
- E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, State-independent quantum contextuality with single photons, Phys. Rev. Lett. 103, 160405 (2009).
- R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, Experimental non-classicality of an indivisible quantum system, Nature (London) 474, 490 (2011).
- C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, State-independent experimental test of quantum contextuality in an indivisible system, Phys. Rev. Lett. 109, 150401 (2012).
- V. D’Ambrosio, I. Herbauts, E. Amselem, E. Nagali, M. Bourennane, F. Sciarrino, and A. Cabello, Experimental implementation of a Kochen-Specker set of quantum tests, Phys. Rev. X 3, 011012 (2013).
- J. Ahrens, E. Amselem, A. Cabello, and M. Bourennane, Two fundamental experimental tests of nonclassicality with qutrits, Sci. Rep. 3, 2170 (2013).
- Y. Hasegawa, R. Loidl, M. Baron, and H. Rauch, Violation of a Bell-like inequality in single-neutron inteferometry, Nature (London) 425, 45 (2003).
- H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, Experimental test of quantum contextuality in neutron interferometry, Phys. Rev. Lett. 103, 040403 (2009).
- G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, State-independent experimental test of quantum contextuality, Nature (London) 460, 494 (2009).
- X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-l. Deng, C. Shen, L.-M. Duan, and K. Kim, State-independent experimental test of quantum contextuality with a single trapped ion, Phys. Rev. Lett. 110, 070401 (2013).
- F. M. Leupold, M. Malinowski, C. Zhang, V. Negnevitsky, A. Cabello, J. Alonso, and J. P. Home, Sustained state-independent quantum contextual correlations from a single ion, Phys. Rev. Lett. 120, 180401 (2018).
- P. Wang, J. Zhang, C.-Y. Luan, M. Um, Y. Wang, M. Qiao, T. Xie, J.-N. Zhang, A. Cabello, and K. Kim, Significant loophole-free test of Kochen-Specker contextuality using two species of atomic ions, Sci. Adv. 8, eabk1660 (2022).
- O. Moussa, C. A. Ryan, D. G. Cory, and R. Laflamme, Testing contextuality on quantum ensembles with one clean qubit, Phys. Rev. Lett. 104, 160501 (2010).
- M. Jerger, Y. Reshitnyk, M. Oppliger, A. Potočnik, M. Mondal, A. Wallraff, K. Goodenough, S. Wehner, K. Juliusson, N. K. Langford, and A. Fedorov, Contextuality without nonlocality in a superconducting quantum system, Nat. Commun. 7, 12930 (2016).
- S. B. van Dam, J. Cramer, T. H. Taminiau, and R. Hanson, Multipartite entanglement generation and contextuality tests using nondestructive three-qubit parity measurements, Phys. Rev. Lett. 123, 050401 (2019).
- J. Thompson, P. Kurzyński, S.-Y. Lee, A. Soeda, and D. Kaszlikowski, Recent advances in contextuality tests, Open Syst. Inf. Dyn. 23, 1650009 (2016).
- C. Budroni, A. Cabello, O. Gühne, M. Kleinmann, and J.-r. Larsson, Kochen-Specker contextuality, Rev. Mod. Phys. 94, 045007 (2022).
- M. Genovese, Research on hidden variable theories: A review of recent progresses, Phys. Rep. 413, 319 (2005).
- M. Fabbrichesi, R. Floreanini, and L. Marzola, About testing Bell locality at colliders, arXiv:2503.18535.
- A. Cabello, S. Severini, and A. Winter, Graph-theoretic approach to quantum correlations, Phys. Rev. Lett. 112, 040401 (2014).
- A. Cabello, M. Kleinmann, and J. R. Portillo, Quantum state-independent contextuality requires 13 rays, J. Phys. A 49, 38LT01 (2016).
- A. A. Klyachko, M. A. Can, S. Binicioglu, and A. S. Shumovsky, Simple test for hidden variables in spin-1 systems, Phys. Rev. Lett. 101, 020403 (2008).
- P. Kurzyński and D. Kaszlikowski, Contextuality of almost all qutrit states can be revealed with nine observables, Phys. Rev. A 86, 042125 (2012).
- S. Yu and C. H. Oh, State-independent proof of Kochen-Specker theorem with 13 rays, Phys. Rev. Lett. 108, 030402 (2012).
- J. Ahrens, E. Amselem, A. Cabello, and M. Bourennane, Two fundamental experimental tests of nonclassicality with qutrits, arXiv:1301.2887.
- A. Cabello, Experimentally testable state-independent quantum contextuality, Phys. Rev. Lett. 101, 210401 (2008).
- N. D. Mermin, Simple unified form for the major no-hidden-variables theorems, Phys. Rev. Lett. 65, 3373 (1990).
- A. Peres, Incompatible results of quantum measurements, Phys. Lett. A 151, 107 (1990).
- A. Peres, Two simple proofs of the Kochen-Specker theorem, J. Phys. A 24, L175 (1991).
- Y. Nambu, Proposed experimental test for proving quantum contextuality with non-entangled photons, arXiv:0805.3398.
- J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969).
- A. Cabello, Converting contextuality into nonlocality, Phys. Rev. Lett. 127, 070401 (2021).
- S. Abramsky and A. Brandenburger, The sheaf-theoretic structure of non-locality and contextuality, New J. Phys. 13, 113036 (2011).
- M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Quantum contextuality of spin-1 massive particles, arXiv:2503.14587.
- J. A. Aguilar-Saavedra and J. Bernabeu, polarisation beyond helicity fractions in top quark decays, Nucl. Phys. B840, 349 (2010).
- G. Aad et al. (ATLAS Collaboration), Measurement of the polarisation of bosons produced in top-quark decays using dilepton events at with the ATLAS experiment, Phys. Lett. B 843, 137829 (2023).
- J. Nakamura, Polarisations of the and bosons in the processes and , J. High Energy Phys. 08 (2017) 008.
- K. Rao, S. D. Rindani, P. Sarmah, and B. Singh, polarization at an collider and properties of decay-lepton angular asymmetries, Proc. Indian Natl. Sci. Acad., Part A 90, 664 (2024).
- 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).
- J. A. Aguilar-Saavedra, A. Bernal, J. A. Casas, and J. M. Moreno, Testing entanglement and Bell inequalities in , Phys. Rev. D 107, 016012 (2023).
- A. Abulencia et al. (CDF Collaboration), Polarization of and mesons produced in collisions at , Phys. Rev. Lett. 99, 132001 (2007).
- R. Aaij et al. (LHCb Collaboration), Measurement of the polarization amplitudes in decays, Phys. Rev. D 88, 052002 (2013).
- R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
- M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Bell inequality is violated in decays, Phys. Rev. D 109, L031104 (2024).
- R. Aaij et al. (LHCb Collaboration), Measurement of asymmetries and polarisation fractions in decays, J. High Energy Phys. 07 (2015) 166.
- K. F. Chen et al. (Belle Collaboration), Measurement of polarization and triple-product correlations in decays, Phys. Rev. Lett. 94, 221804 (2005).
- R. Aaij et al. (LHCb Collaboration), Measurement of polarization amplitudes and asymmetries in , J. High Energy Phys. 05 (2014) 069.
- M. Ablikim et al. (BESIII Collaboration), Helicity amplitude analysis of , J. High Energy Phys. 05 (2023) 069.
- M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Bell inequality is violated in charmonium decays, Phys. Rev. D 110, 053008 (2024).
- W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
- M. Ablikim et al. (BESIII Collaboration), Precise measurements of decay parameters and asymmetry with entangled pairs, Phys. Rev. Lett. 129, 131801 (2022).
- M. Ablikim et al. (BESIII Collaboration), Measurement of transverse polarization in collisions at , J. High Energy Phys. 10 (2023) 081; 12 (2023) 80.
- M. Ablikim et al. (BESIII Collaboration), and polarization in the and decays, Phys. Rev. Lett. 125, 052004 (2020).
- 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).
- M. Fabbrichesi, R. Floreanini, and G. Panizzo, Testing Bell inequalities at the LHC with top-quark pairs, Phys. Rev. Lett. 127, 161801 (2021).
- 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).
- 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).
- Z. Dong, D. Gonçalves, K. Kong, and A. Navarro, Entanglement and Bell inequalities with boosted , Phys. Rev. D 109, 115023 (2024).
- 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.
- G. Aad et al. (ATLAS Collaboration), Observation of quantum entanglement with top quarks at the ATLAS detector, Nature (London) 633, 542 (2024).
- A. Hayrapetyan et al. (CMS Collaboration), Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using events from proton-proton collisions at , Phys. Rev. D 110, 112016 (2024).
- 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).
- R. D. Ball et al. (PDF4LHC Working Group), The PDF4LHC21 combination of global PDF fits for the LHC Run III, J. Phys. G 49, 080501 (2022).
- W. Bernreuther and Z.-G. Si, Distributions and correlations for top quark pair production and decay at the Tevatron and LHC, Nucl. Phys. B837, 90 (2010).
- M. Czakon, A. Mitov, and R. Poncelet, NNLO QCD corrections to leptonic observables in top-quark pair production and decay, J. High Energy Phys. 05 (2021) 212.
- R. Frederix, I. Tsinikos, and T. Vitos, Probing the spin correlations of production at NLO , Eur. Phys. J. C 81, 817 (2021).
- K. Ehatäht, M. Fabbrichesi, L. Marzola, and C. Veelken, Probing entanglement and testing Bell inequality violation with at Belle II, Phys. Rev. D 109, 032005 (2024).
- M. Fabbrichesi and L. Marzola, Dipole momenta and compositeness of the lepton at Belle II, Phys. Rev. D 109, 095026 (2024).
- M. Fabbrichesi and L. Marzola, Quantum tomography with leptons at the FCC-ee: Entanglement, Bell inequality violation, , and anomalous couplings, Phys. Rev. D 110, 076004 (2024).
- T. Han, M. Low, and Y. Su, Entanglement and Bell Nonlocality in at the BEPC, arXiv:2501.04801.
- 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).
- Y. Zhang, B.-H. Zhou, Q.-B. Liu, S. Li, S.-C. Hsu, T. Han, M. Low, and T. A. Wu, Entanglement and Bell nonlocality in at the LHC using machine learning for neutrino reconstruction, arXiv:2504.01496.