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arXiv:2406.04402 · Physical review. D/Physical review. D.

Entanglement and Bell nonlocality with bottom-quark pairs at hadron colliders

Y. Afik, Yevgeny Kats, Juan Ramón Muñoz de Nova, Abner Soffer, David Uzan

Published May 29, 2025• 24 citations
arXivHTMLPDF

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 B parking dataset, while observation of Bell nonlocality may become feasible at the high-luminosity phase of the LHC.

DOI
10.1103/fhkc-kfhr

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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.
Abstract 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 − 0.029 + 0.026 ( − 0.467 − 0.029 + 0.026 ) 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.
The ATLAS Collaboration has recently announced the first observation of quantum entanglement in top quark pair production at the Large Hadron Collider (LHC). This work briefly reviews the experimental status of top quark pair spin correlations and highlights the distinctions between classical and quantum correlations. A proposed criterion for detecting spin entanglement in top quark pairs is outlined, along with the experimental strategy to observe this effect, culminating in the positive results of the ATLAS measurement.
Correlations between the spins of top-quark pairs produced at a collider can be used to probe quantum entanglement at energies never explored so far. We show how the measurement of a single observable can provide a test of the violation of a Bell inequality at the 98% C.L. with the statistical uncertainty of the data already collected at the Large Hadron Collider, and at the 99.99% C.L. with the higher luminosity of the next run. Detector acceptance, efficiency, and migration effects are taken into account. The test relies on the spin correlations alone and does not require the determination of probabilities-in contrast to all other tests of Bell inequalities.
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.