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arXiv:2510.13743 · European Physical Society Conference on High Energy Physics (EPS-HEP)

Measurements of top quark properties in CMS: $t\bar{t}$ spin density matrix, quantum entanglement and quantum magic

E. Yazgan

Published Jan 28, 2026• 1 citation
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Abstract

Polarization and spin correlation measurements of top quark-antiquark ($t\bar{t}$) pairs provide tests of the standard model, but also new ways to test quantum mechanics with unstable particles at highest energies ever produced in a laboratory. Recent $t\bar{t}$ spin correlation measurements and the tests they enable, made with the CMS detector at the CERN LHC Run 2, are presented. The measurements summarized include the full spin density matrix measurement of top quark pairs using events with a single lepton and jets in the final state. Spin correlation measurements in specific phase space regions allow the observation of the entanglement phenomenon, and the measurement of quantum magic. From the measured spin correlation at the $t\bar{t}$ production threshold and high $t\bar{t}$ mass, entanglement is observed with a large fraction of the $t\bar{t}$ decays being spacelike separated. The observation of entanglement in $t\bar{t}$ events with two high transverse momentum leptons of opposite charge is also presented. Finally, the first TeV-scale experimental measurement of quantum magic, an important variable for the characterization of quantum states in quantum information science, is presented. These measurements provide one of the first connections between quantum information science and particle physics, and show the potential of collider experiments in the studies of the foundations of quantum mechanics.

DOI
10.22323/1.485.0273

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Measurements of top quark properties in CMS: ttˉt\bar{t}ttˉ spin density matrix, quantum entanglement and quantum magic
Polarization and spin correlation measurements of top quark-antiquark (ttˉt\bar{t}ttˉ) pairs provide tests of the standard model, but also new ways to test quantum mechanics with unstable particles at highest energies ever produced in a laboratory. Recent ttˉt\bar{t}ttˉ spin correlation measurements and the tests they enable, made with the CMS detector at the CERN LHC Run 2, are presented. The measurements summarized include the full spin density matrix measurement of top quark pairs using events with a single lepton and jets in the final state. Spin correlation measurements in specific phase space regions allow the observation of the entanglement phenomenon, and the measurement of quantum magic. From the measured spin correlation at the ttˉt\bar{t}ttˉ production threshold and high ttˉt\bar{t}ttˉ mass, entanglement is observed with a large fraction of the ttˉt\bar{t}ttˉ decays being spacelike separated. The observation of entanglement in ttˉt\bar{t}ttˉ events with two high transverse momentum leptons of opposite charge is also presented. Finally, the first TeV-scale experimental measurement of quantum magic, an important variable for the characterization of quantum states in quantum information science, is presented. These measurements provide one of the first connections between quantum information science and particle physics, and show the potential of collider experiments in the studies of the foundations of quantum mechanics.
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.
Recent results from the Large Hadron Collider have demonstrated quantum entanglement of top quark-antiquark pairs using the spin degrees of freedom. Based on the doubly differential measurement of the spin density matrix of the top quark and antiquark performed by the CMS collaboration in the helicity and beam bases, we evaluate a set of quantum observables, including discord, steerability, Bell correlation, and magic. These observables allow for a quantitative characterization of the quantum correlations present in a top quark-antiquark system, thus enabling an interpretation of collider data in terms of quantum states and their properties. Discord is observed to be greater than zero with a significance of more than 5 standard deviations (σσσ) in several regions of phase space, some of which correspond to separable quantum states. Evidence for steerability is established for the first time in a high-energy system, with a significance of more than 3σσσ. No Bell correlation is observed within the currently probed phase space, in agreement with the theoretical prediction. These results experimentally corroborate the hierarchy of quantum correlations in top quarks with discord being the most basic form of quantum correlation, followed by entanglement, steerability, and Bell correlation. The significance of nonzero magic, which is a complementary observable to the quantum correlation hierarchy, is found to exceed 5σσσ in several regions of phase space.
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.
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.
Entanglement is a key feature of quantum mechanics1,2,3^{1,2,3}1,2,3, with applications in fields such as metrology, cryptography, quantum information and quantum computation4,5,6,7,8^{4,5,6,7,8}4,5,6,7,8. It has been observed in a wide variety of systems and length scales, ranging from the microscopic9,10,11,12,13^{9,10,11,12,13}9,10,11,12,13 to the macroscopic14,15,16^{14,15,16}14,15,16. 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\sqrt{s} = 13\text{ TeV}s​=13 TeV and an integrated luminosity of 140 inverse femtobarns (fb)−1140\text{ inverse femtobarns (fb)}^{-1}140 inverse femtobarns (fb)−1 recorded with the ATLAS experiment. Spin entanglement is detected from the measurement of a single observable DDD, 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.)D = -0.537 \pm 0.002 \text{ (stat.)} \pm 0.019 \text{ (syst.)}D=−0.537±0.002 (stat.)±0.019 (syst.) for . 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.