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arXiv:2505.02902 · Journal of High Energy Physics

Local vs. nonlocal entanglement in top-quark pairs at the LHC

Marco E. Fabbrichesi, Roberto Floreanini B, Luca Marzola

Published Nov 4, 2025• 8 citations
arXivHTMLPDF

Abstract

A bstract We show that the entanglement observed in top-antitop quark spin states at the LHC is local in the energy region close to the production threshold. In contrast, nonlocal entanglement is observed in the central boosted region defined by a top-quark pair invariant mass $${m}_{t\overline{t} }>{8}00$$ GeV and scattering angles Θ satisfying |cos Θ| < 0 . 2. This makes top-quark pairs a unique laboratory for studying the interplay between entanglement and Bell locality. The locality of entanglement near the production threshold is further supported by a recent CMS analysis, which reports a significance of more than 5 σ . We also demonstrate that there exists a kinematic region where the spin states of the top-antitop quark are separable, yet they exhibit non-zero discord and magic.

DOI
10.1007/jhep11(2025)005

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A bstract We show that the entanglement observed in top-antitop quark spin states at the LHC is local in the energy region close to the production threshold. In contrast, nonlocal entanglement is observed in the central boosted region defined by a top-quark pair invariant mass mtt‾>800{m}_{t\overline{t} }>{8}00mtt​>800 GeV and scattering angles Θ satisfying |cos Θ| < 0 . 2. This makes top-quark pairs a unique laboratory for studying the interplay between entanglement and Bell locality. The locality of entanglement near the production threshold is further supported by a recent CMS analysis, which reports a significance of more than 5 σ . We also demonstrate that there exists a kinematic region where the spin states of the top-antitop quark are separable, yet they exhibit non-zero discord and magic.
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 B parking dataset, while observation of Bell nonlocality may become feasible at the high-luminosity phase of the LHC.
We investigate quantum coherence in the spin degrees of freedom of top--antitop pairs produced at the LHC using the l1l_1l1​-norm of coherence in the helicity basis. Combining Standard Model predictions with the spin density matrix reconstructed from the CMS measurement of top-quark spin correlation coefficients, we study the dependence of coherence on the invariant mass MttˉM_{t\bar t}Mttˉ​ and production angle. To quantify the experimental precision of the extracted coherence, we propagate the measured uncertainties and covariance matrix of the spin-correlation coefficients through a Monte Carlo procedure. We find a non-monotonic kinematic dependence: coherence is large near the production threshold, is reduced in the intermediate-mass region, and increases again in boosted central events. The theoretical predictions are in good agreement with the CMS determinations in all three kinematic regions. Moreover, the experimentally reconstructed coherence is nonzero with a significance exceeding 5σ5σ5σ in each region. In particular, in the intermediate-mass region, 400<Mttˉ<600 GeV400<M_{t\bar t}<600~\mathrm{GeV}400<Mttˉ​<600 GeV, we obtain Cl1=0.597±0.037C_{l_1}=0.597\pm0.037Cl1​​=0.597±0.037. This result is especially noteworthy because previous analyses of the same reconstructed top-quark spin density matrix found concurrence and negativity, both entanglement measures, to be consistent with zero, 0.00±0.020.00\pm0.020.00±0.02, in this kinematic region. The persistence of sizable coherence where entanglement is not experimentally certified demonstrates that coherence provides complementary information on the off-diagonal helicity-interference structure of the top-quark spin density matrix. Our results establish quantum coherence as an experimentally accessible and statistically robust observable for probing the quantum structure of top-quark pair production at the LHC.
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We investigate quantum steering and Bell nonlocality in top-quark pair production at the LHC near threshold. The toponium contribution strengthens the spin-singlet component and substantially enhances the entanglement between the two quark spins. With current LHC data, quantum steering appears observable with a statistical significance around 10σ10σ10σ. For Bell nonlocality, the statistical significance can also be high close to threshold, reaching about 9σ9σ9σ, although the feasibility of such a measurement will depend crucially on the control of systematic uncertainties.
Abstract Entanglement is a key feature of quantum mechanics1–3, with applications in fields such as metrology, cryptography, quantum information and quantum computation4–8. It has been observed in a wide variety of systems and length scales, ranging from the microscopic9–13 to the macroscopic14–16. However, entanglement remains largely unexplored at the highest accessible energy scales. Here we report the highest-energy observation of entanglement, in top–antitop quark events produced at the Large Hadron Collider, using a proton–proton collision dataset with a centre-of-mass energy of √s = 13 TeV and an integrated luminosity of 140 inverse femtobarns (fb)−1 recorded with the ATLAS experiment. Spin entanglement is detected from the measurement of a single observable D, inferred from the angle between the charged leptons in their parent top- and antitop-quark rest frames. The observable is measured in a narrow interval around the top–antitop quark production threshold, at which the entanglement detection is expected to be significant. It is reported in a fiducial phase space defined with stable particles to minimize the uncertainties that stem from the limitations of the Monte Carlo event generators and the parton shower model in modelling top-quark pair production. The entanglement marker is measured to be D = −0.537 ± 0.002 (stat.) ± 0.019 (syst.) for 340 GeV<mttˉ<380 GeV340\,{\rm{GeV}} < {m}_{t\bar{t}} < 380\,{\rm{GeV}}340GeV<mttˉ​<380GeV 340 GeV < m t t ¯ < 380 GeV . The observed result is more than five standard deviations from a scenario without entanglement and hence constitutes the first observation of entanglement in a pair of quarks and the highest-energy observation of entanglement so far.
Entanglement is an intrinsic property of quantum mechanics and is predicted to be exhibited in the particles produced at the Large Hadron Collider. A measurement of the extent of entanglement in top quark-antiquark (t¯t) events produced in proton–proton collisions at a center-of-mass energy of 13 TeV is performed with the data recorded by the CMS experiment at the CERN LHC in 2016, and corresponding to an integrated luminosity of 36.3 fb−1 . The events are selected based on the presence of two leptons with opposite charges and high transverse momentum. An entanglement-sensitive observable D is derived from the top quark spin-dependent parts of the t¯t production density matrix and measured in the region of the t¯t production threshold. Values of D < −1/3 are evidence of entanglement and D is observed (expected) to be −0.480+0.026 −0.029 (−0.467+0.026 −0.029) at the parton level. With an observed significance of 5.1 standard deviations with respect to the non-entangled hypothesis, this provides observation of quantum mechanical entanglement within t¯t pairs in this phase space. This measurement provides a new probe of quantum mechanics at the highest energies ever produced.