- Letter
- Open Access
Entanglement and Bell nonlocality with bottom-quark pairs at hadron colliders
Phys. Rev. D 111, L111902 – Published 13 June, 2025
DOI: https://doi.org/10.1103/fhkc-kfhr
Abstract
It has been shown that entanglement and Bell nonlocality, which are key concepts in quantum mechanics, can be probed in high-energy colliders via processes of fundamental particle scattering. In fact, the ATLAS and CMS Collaborations have measured entanglement using top-quark pairs produced in proton-proton collisions at the LHC. Recently, it was shown that spin correlations can be measured in pairs of bottom quarks at the LHC, despite the fact that bottom quarks, unlike top quarks, hadronize before decaying. Here, we demonstrate that quantum correlations can also be studied using bottom-quark pairs, and analyze the feasibility of the observation of entanglement and Bell nonlocality in several collider experiments. Given the low mass of the bottom quark relative to typical energies accessible at the LHC, many of the bottom-quark pairs are in the ultrarelativistic regime, where they can exhibit strong spin entanglement. We find that entanglement of bottom-quark pairs may be measurable even with the LHC Run 2 data, especially with the CMS parking dataset, while observation of Bell nonlocality may become feasible at the high-luminosity phase of the LHC.
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References (121)
- A. Einstein, B. Podolsky, and N. Rosen, Can quantum mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777 (1935).
- E. Schrodinger, Discussion of probability relations between separated systems, Proc. Cambridge Philos. Soc. 31, 555 (1935).
- J. S. Bell, On the Einstein-Podolsky-Rosen paradox, Phys. Phys. Fiz. 1, 195 (1964).
- A. Aspect, P. Grangier, and G. Roger, Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: A new violation of Bell’s inequalities, Phys. Rev. Lett. 49, 91 (1982).
- E. Hagley, X. Maître, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche, Generation of Einstein-Podolsky-Rosen pairs of atoms, Phys. Rev. Lett. 79, 1 (1997).
- M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, Measurement of the entanglement of two superconducting qubits via state tomography, Science 313, 1423 (2006).
- W. Pfaff, T. H. Taminiau, L. Robledo, H. Bernien, M. Markham, D. J. Twitchen, and R. Hanson, Demonstration of entanglement-by-measurement of solid-state qubits, Nat. Phys. 9, 29 (2013).
- A. Go et al. (Belle Collaboration), Measurement of EPR-type flavour entanglement in decays, Phys. Rev. Lett. 99, 131802 (2007).
- B. Julsgaard, A. Kozhekin, and E. S. Polzik, Experimental long-lived entanglement of two macroscopic objects, Nature (London) 413, 400 (2001).
- K. Lee, M. Sprague, B. Sussman, J. Nunn, N. Langford, X.-M. Jin, T. Champion, P. Michelberger, K. Reim, D. England, D. Jaksch, and I. Walmsley, Entangling macroscopic diamonds at room temperature, Science 334, 1253 (2011).
- C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Woolley, and M. A. Sillanpää, Stabilized entanglement of massive mechanical oscillators, Nature (London) 556, 478 (2018).
- S. Storz et al., Loophole-free Bell inequality violation with superconducting circuits, Nature (London) 617, 265 (2023).
- N. A. Törnqvist, Suggestion for Einstein-Podolsky-Rosen experiments using reactions like , Found. Phys. 11, 171 (1981).
- N. A. Törnqvist, The decay as an Einstein-Podolsky-Rosen experiment, Phys. Lett. 117A, 1 (1986).
- P. Privitera, Decay correlations in as a test of quantum mechanics, Phys. Lett. B 275, 172 (1992).
- S. A. Abel, M. Dittmar, and H. K. Dreiner, Testing locality at colliders via Bell’s inequality?, Phys. Lett. B 280, 304 (1992).
- Y. Afik and J. R. Muñoz 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).
- Y. Afik and J. R. Muñoz de Nova, Quantum information with top quarks in QCD, Quantum 6, 820 (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).
- Y. Afik and J. R. Muñoz de Nova, Quantum discord and steering in top quarks at the LHC, Phys. Rev. Lett. 130, 221801 (2023).
- 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.
- J. A. Aguilar-Saavedra, Postdecay quantum entanglement in top pair production, Phys. Rev. D 108, 076025 (2023).
- K. Cheng, T. Han, and M. Low, Optimizing fictitious states for Bell inequality violation in bipartite qubit systems with applications to the system, Phys. Rev. D 109, 116005 (2024).
- Z. Dong, D. Gonçalves, K. Kong, and A. Navarro, Entanglement and Bell inequalities with boosted , Phys. Rev. D 109, 115023 (2024).
- J. A. Aguilar-Saavedra, A closer look at post-decay entanglement, Phys. Rev. D 109, 096027 (2024).
- J. A. Aguilar-Saavedra and J. A. Casas, Entanglement autodistillation from particle decays, Phys. Rev. Lett. 133, 111801 (2024).
- C. D. White and M. J. White, Magic states of top quarks, Phys. Rev. D 110, 116016 (2024).
- 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), Observation of quantum entanglement in top quark pair production in proton–proton collisions at , Rep. Prog. Phys. 87, 117801 (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. Blasone, F. Dell’Anno, S. De Siena, and F. Illuminati, Entanglement in neutrino oscillations, Europhys. Lett. 85, 50002 (2009).
- J. A. Formaggio, D. I. Kaiser, M. M. Murskyj, and T. E. Weiss, Violation of the Leggett-Garg inequality in neutrino oscillations, Phys. Rev. Lett. 117, 050402 (2016).
- F. Ming, X.-K. Song, J. Ling, L. Ye, and D. Wang, Quantification of quantumness in neutrino oscillations, Eur. Phys. J. C 80, 275 (2020).
- M. Blasone, S. De Siena, and C. Matrella, Wave packet approach to quantum correlations in neutrino oscillations, Eur. Phys. J. C 81, 660 (2021).
- 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).
- M. M. Altakach, P. Lamba, F. Maltoni, K. Mawatari, and K. Sakurai, Quantum information and measurement in at future lepton colliders, Phys. Rev. D 107, 093002 (2023).
- 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, Quantum tomography with leptons at the FCC-ee: Entanglement, Bell inequality violation, , and anomalous couplings, Phys. Rev. D 110, 076004 (2024).
- A. J. Barr, Testing Bell inequalities in Higgs boson decays, Phys. Lett. B 825, 136866 (2022).
- A. J. Barr, P. Caban, and J. Rembieliński, Bell-type inequalities for systems of relativistic vector bosons, Quantum 7, 1070 (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).
- J. A. Aguilar-Saavedra, Laboratory-frame tests of quantum entanglement in , Phys. Rev. D 107, 076016 (2023).
- A. Bernal, P. Caban, and J. Rembieliński, Entanglement and Bell inequalities violation in with anomalous coupling, Eur. Phys. J. C 83, 1050 (2023).
- R. A. Morales, Exploring Bell inequalities and quantum entanglement in vector boson scattering, Eur. Phys. J. Plus 138, 1157 (2023).
- F. Fabbri, J. Howarth, and T. Maurin, Isolating semi-leptonic decays for Bell inequality tests, Eur. Phys. J. C 84, 20 (2024).
- 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).
- O. K. Baker and D. E. Kharzeev, Thermal radiation and entanglement in proton-proton collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. D 98, 054007 (2018).
- Z. Tu, D. E. Kharzeev, and T. Ullrich, Einstein-Podolsky-Rosen paradox and quantum entanglement at subnucleonic scales, Phys. Rev. Lett. 124, 062001 (2020).
- W. Gong, G. Parida, Z. Tu, and R. Venugopalan, Measurement of Bell-type inequalities and quantum entanglement from -hyperon spin correlations at high energy colliders, Phys. Rev. D 106, L031501 (2022).
- A. Florio, D. Frenklakh, K. Ikeda, D. Kharzeev, V. Korepin, S. Shi, and K. Yu, Real-time nonperturbative dynamics of jet production in Schwinger model: Quantum entanglement and vacuum modification, Phys. Rev. Lett. 131, 021902 (2023).
- J. Barata, W. Gong, and R. Venugopalan, Realtime dynamics of hyperon spin correlations from string fragmentation in a deformed four-flavor Schwinger model, Phys. Rev. D 109, 116003 (2024).
- M. Hentschinski, D. E. Kharzeev, K. Kutak, and Z. Tu, QCD evolution of entanglement entropy, Rep. Prog. Phys. 87, 120501 (2024).
- R. von Kuk, K. Lee, J. K. Michel, and Z. Sun, Towards a quantum information theory of hadronization: Dihadron fragmentation and neutral polarization in heavy baryons, arXiv:2503.22607.
- Y. Kats and D. Uzan, Prospects for measuring quark polarization and spin correlations in and samples at the LHC, J. High Energy Phys. 03 (2024) 063.
- G. Aad et al. (ATLAS Collaboration), The ATLAS experiment at the CERN large hadron collider, J. Instrum. 3, S08003 (2008).
- S. Chatrchyan et al. (CMS Collaboration), The CMS experiment at the CERN LHC, J. Instrum. 3, S08004 (2008).
- A. A. Alves, Jr. et al. (LHCb Collaboration), The LHCb detector at the LHC, J. Instrum. 3, S08005 (2008).
- M. Neubert, Heavy quark effective theory, Subnucl. Ser. 34, 98 (1997), arXiv:hep-ph/9610266.
- J. G. Korner, A. Pilaftsis, and M. M. Tung, One-loop QCD mass effects in the production of polarized bottom and top quarks, Z. Phys. C 63, 575 (1994).
- W. Bernreuther, A. Brandenburg, Z. G. Si, and P. Uwer, Top quark pair production and decay at hadron colliders, Nucl. Phys. B690, 81 (2004).
- M. Baumgart and B. Tweedie, A new twist on top quark spin correlations, J. High Energy Phys. 03 (2013) 117.
- W. Bernreuther and A. Brandenburg, Tracing violation in the production of top quark pairs by multiple TeV proton proton collisions, Phys. Rev. D 49, 4481 (1994).
- W. Bernreuther, M. Flesch, and P. Haberl, Signatures of Higgs bosons in the top quark decay channel at hadron colliders, Phys. Rev. D 58, 114031 (1998).
- T. Mannel and G. A. Schuler, Semileptonic decays of bottom baryons at LEP, Phys. Lett. B 279, 194 (1992).
- F. E. Close, J. G. Körner, R. J. N. Phillips, and D. J. Summers, Report of the b-fragmentation working group. Section 5: B polarization at LEP, J. Phys. G 18, 1703 (1992).
- A. F. Falk and M. E. Peskin, Production, decay, and polarization of excited heavy hadrons, Phys. Rev. D 49, 3320 (1994).
- M. Galanti, A. Giammanco, Y. Grossman, Y. Kats, E. Stamou, and J. Zupan, Heavy baryons as polarimeters at colliders, J. High Energy Phys. 11 (2015) 067.
- D. Buskulic et al. (ALEPH Collaboration), Measurement of the polarization in Z decays, Phys. Lett. B 365, 437 (1996).
- G. Abbiendi et al. (OPAL Collaboration), Measurement of the average polarization of baryons in hadronic decays, Phys. Lett. B 444, 539 (1998).
- P. Abreu et al. (DELPHI Collaboration), polarization in decays at LEP, Phys. Lett. B 474, 205 (2000).
- A. Metz and A. Vossen, Parton fragmentation functions, Prog. Part. Nucl. Phys. 91, 136 (2016).
- K. Chen, G. R. Goldstein, R. L. Jaffe, and X.-D. Ji, Probing quark fragmentation functions for spin- baryon production in unpolarized annihilation, Nucl. Phys. B445, 380 (1995).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/fhkc-kfhr which includes Refs. [76,77], for additional details.
- A. Andronic, F. Beutler, P. Braun-Munzinger, K. Redlich, and J. Stachel, Statistical hadronization of heavy flavor quarks in elementary collisions: Successes and failures, Phys. Lett. B 678, 350 (2009).
- R. Aaij et al. (LHCb Collaboration), Observation of two resonances in the systems and precise measurement of and properties, Phys. Rev. Lett. 122, 012001 (2019).
- S. Dambach, U. Langenegger, and A. Starodumov, Neutrino reconstruction with topological information, Nucl. Instrum. Methods Phys. Res., Sect. A 569, 824 (2006).
- R. Aaij et al. (LHCb Collaboration), Determination of the quark coupling strength using baryonic decays, Nat. Phys. 11, 743 (2015).
- R. Aaij et al. (LHCb Collaboration), First observation of the decay and a measurement of , Phys. Rev. Lett. 126, 081804 (2021).
- G. Ciezarek, A. Lupato, M. Rotondo, and M. Vesterinen, Reconstruction of semileptonically decaying beauty hadrons produced in high energy collisions, J. High Energy Phys. 02 (2017) 021.
- S. Dambach, CMS pixel module readout optimization and study of the lifetime in the semileptonic decay mode, Ph.D. thesis, Heidelberg University, 2009.
- W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
- 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).
- R. Horodecki, P. Horodecki, and M. Horodecki, Violating Bell inequality by mixed spin- states: Necessary and sufficient condition, Phys. Lett. A 200, 340 (1995).
We have checked that other procedures to evaluate the Bell nonlocality marker, such as directly averaging in phase space or alternative basis choices, do not substantially improve the significance of the observation.
- R. D. Ball et al. (NNPDF Collaboration), Parton distributions for the LHC Run II, J. High Energy Phys. 04 (2015) 040.
- I. Béjar Alonso et al., High-luminosity large hadron collider (HL-LHC): Technical design report, Technical Report No. CERN-2020-010, CERN, Geneva, 2020.
- LHCb Collaboration, Framework TDR for the LHCb Upgrade II: Opportunities in flavour physics, and beyond, in the HL-LHC era, Technical Reports No. CERN-LHCC-2021-012, No. LHCB-TDR-023, CERN, Geneva, 2021.
- R. Bainbridge (CMS Collaboration), Recording and reconstructing 10 billion unbiased b hadron decays in CMS, EPJ Web Conf. 245, 01025 (2020).
- A. Hayrapetyan et al. (CMS Collaboration), Enriching the physics program of the CMS experiment via data scouting and data parking, Phys. Rep. 1115, 678 (2025).
- A. Hayrapetyan et al. (CMS Collaboration), Test of lepton flavor universality in and decays in proton-proton collisions at , Rep. Prog. Phys. 87, 077802 (2024).
- A. Hayrapetyan et al. (CMS Collaboration), Search for long-lived heavy neutrinos in the decays of B mesons produced in proton-proton collisions at , J. High Energy Phys. 06 (2024) 183.
- J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, J. High Energy Phys. 07 (2014) 079.
- R. D. Ball et al. (NNPDF Collaboration), Parton distributions from high-precision collider data, Eur. Phys. J. C 77, 663 (2017).
- T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, An introduction to pythia 8.2, Comput. Phys. Commun. 191, 159 (2015).
- M. Cacciari, G. P. Salam, and G. Soyez, The anti- jet clustering algorithm, J. High Energy Phys. 04 (2008) 063.
- M. Cacciari, G. P. Salam, and G. Soyez, fastJet user manual, Eur. Phys. J. C 72, 1896 (2012).
- G. Aad et al. (ATLAS Collaboration), Performance of the ATLAS muon triggers in Run 2, J. Instrum. 15, P09015 (2020).
- ATLAS Collaboration, Expected performance of the ATLAS detector at the High-Luminosity LHC, Technical Report No. ATL-PHYS-PUB-2019-005, CERN, Geneva, 2019.
- R. Aaij et al. (LHCb Collaboration), Measurement of hadron fractions in 13 TeV collisions, Phys. Rev. D 100, 031102 (2019).
- R. Aaij et al. (LHCb Collaboration), Enhanced production of baryons in high-multiplicity collisions at , Phys. Rev. Lett. 132, 081901 (2024).
- R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
- R. Aaij et al. (LHCb Collaboration), Test of lepton universality with decays, J. High Energy Phys. 08 (2017) 055.
- R. Aaij et al. (LHCb Collaboration), Amplitude analysis of the decay and baryon polarization measurement in semileptonic beauty hadron decays, Phys. Rev. D 108, 012023 (2023).
- A. Abada et al. (FCC Collaboration), FCC-ee: The lepton collider: Future circular collider conceptual design report volume 2, Eur. Phys. J. Special Topics 228, 261 (2019).
- A. Abada et al. (FCC Collaboration), FCC-hh: The hadron collider: Future circular collider conceptual design report volume 3, Eur. Phys. J. Special Topics 228, 755 (2019).
- M. Benedikt, A. Blondel, P. Janot, M. Mangano, and F. Zimmermann, Future circular colliders succeeding the LHC, Nat. Phys. 16, 402 (2020).
- L. Adamczyk et al. (STAR Collaboration), Global hyperon polarization in nuclear collisions: Evidence for the most vortical fluid, Nature (London) 548, 62 (2017).
- S. Acharya et al. (ALICE Collaboration), Polarization of and hyperons along the beam direction in Pb-Pb collisions at , Phys. Rev. Lett. 128, 172005 (2022).
- R. Abou Yassine et al. (HADES Collaboration), Measurement of global polarization of hyperons in few-GeV heavy-ion collisions, Phys. Lett. B 835, 137506 (2022).
- M. S. Abdallah et al. (STAR Collaboration), Pattern of global spin alignment of and mesons in heavy-ion collisions, Nature (London) 614, 244 (2023).
- G. Giacalone and E. Speranza, Initial-state-driven spin correlations in high-energy nuclear collisions, arXiv:2502.13102.
- M. Czachor, Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles, Phys. Rev. A 55, 72 (1997).
- R. M. Gingrich and C. Adami, Quantum entanglement of moving bodies, Phys. Rev. Lett. 89, 270402 (2002).
- A. Peres and D. R. Terno, Quantum information and relativity theory, Rev. Mod. Phys. 76, 93 (2004).
- N. Friis, A. R. Lee, K. Truong, C. Sabin, E. Solano, G. Johansson, and I. Fuentes, Relativistic quantum teleportation with superconducting circuits, Phys. Rev. Lett. 110, 113602 (2013).
- J. Rembieliński and P. Caban, Relativistic chiral qubits, their time evolution, and correlations, Phys. Rev. A 99, 022320 (2019).
- F. Giacomini, E. Castro-Ruiz, and Č. Brukner, Relativistic quantum reference frames: The operational meaning of spin, Phys. Rev. Lett. 123, 090404 (2019).
- E. Taillebois and A. Avelar, Relativistic spin operator must be intrinsic, Phys. Lett. A 392, 127166 (2021).
- P. Kurashvili and L. Chotorlishvili, Quantum discord and entropic measures of two relativistic fermions, J. Phys. A 55, 495303 (2022).