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arXiv:2606.30768 · Physical review. D/Physical review. D.

Toponium effects on quantum steering and Bell nonlocality of top quarks

J. A. Aguilar-Saavedra, S. Rodríguez-Benítez

hep-phhep-exquant-phSubmitted Jun 29, 2026• Announced Jul 1, 2026• 0 citations
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Abstract

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 $10σ$. For Bell nonlocality, the statistical significance can also be high close to threshold, reaching about $9σ$, although the feasibility of such a measurement will depend crucially on the control of systematic uncertainties.

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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.
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.
Top quarks have been recently shown to be a promising system to study quantum information at the highest-energy scale available. The current lines of research mostly discuss topics such as entanglement, Bell nonlocality or quantum tomography. Here, we provide the full picture of quantum correlations in top quarks by studying also quantum discord and steering. We find that both phenomena are present at the LHC. In particular, quantum discord in a separable quantum state is expected to be detected with high-statistical significance. Interestingly, due to the singular nature of the measurement process, quantum discord can be measured following its original definition, and the steering ellipsoid can be experimentally reconstructed, both highly demanding measurements in conventional setups. In contrast to entanglement, the asymmetric nature of quantum discord and steering can provide witnesses of CP-violating physics beyond the standard model.
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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.