We investigate the interplay between quantum correlations and multiparameter quantum estimation in top--antitop quark pair production through the gluon-fusion channel. Using the spin density matrix formalism, we construct an effective two-qubit quantum state governed by the relativistic parameters associated with the scattering process. Within the framework of quantum metrology, we derive the quantum Fisher information matrix for the simultaneous estimation of the relativistic velocity parameter and the production angle, and we analyze the corresponding quantum precision bounds. Our results reveal highly nontrivial estimation regimes strongly controlled by relativistic spin correlations and scattering geometry. We further characterize the produced state through the concurrence and demonstrate the existence of strong connections between entanglement structures and multiparameter estimation sensitivity. Finally, we discuss the experimental feasibility of probing these effects at the Large Hadron Collider through spin-correlation observables and reconstructed top--antitop density matrices. Our results identify top--antitop production as a unique relativistic platform for exploring quantum information theory and multiparameter quantum metrology in high-energy physics.
We investigate the interplay between quantum correlations and multiparameter quantum estimation in top--antitop quark pair production through the gluon-fusion channel. Using the spin density matrix formalism, we construct an effective two-qubit quantum state governed by the relativistic parameters associated with the scattering process. Within the framework of quantum metrology, we derive the quantum Fisher information matrix for the simultaneous estimation of the relativistic velocity parameter and the production angle, and we analyze the corresponding quantum precision bounds. Our results reveal highly nontrivial estimation regimes strongly controlled by relativistic spin correlations and scattering geometry. We further characterize the produced state through the concurrence and demonstrate the existence of strong connections between entanglement structures and multiparameter estimation sensitivity. Finally, we discuss the experimental feasibility of probing these effects at the Large Hadron Collider through spin-correlation observables and reconstructed top--antitop density matrices. Our results identify top--antitop production as a unique relativistic platform for exploring quantum information theory and multiparameter quantum metrology in high-energy physics.
Top quarks represent unique high-energy systems since their spin correlations can be measured, thus allowing to study fundamental aspects of quantum mechanics with qubits at high-energy colliders. We present here the general framework of the quantum state of a top-antitop ( tt¯ ) quark pair produced through quantum chromodynamics (QCD) in a high-energy collider. We argue that, in general, the total quantum state that can be probed in a collider is given in terms of the production spin density matrix, which necessarily gives rise to a mixed state. We compute the quantum state of a tt¯ pair produced from the most elementary QCD processes, finding the presence of entanglement and CHSH violation in different regions of phase space. We show that any realistic hadronic production of a tt¯ pair is a statistical mixture of these elementary QCD processes. We focus on the experimentally relevant cases of proton-proton and proton-antiproton collisions, performed at the LHC and the Tevatron, analyzing the dependence of the quantum state with the energy of the collisions. We provide experimental observables for entanglement and CHSH-violation signatures. At the LHC, these signatures are given by the measurement of a single observable, which in the case of entanglement represents the violation of a Cauchy-Schwarz inequality. We extend the validity of the quantum tomography protocol for the tt¯ pair proposed in the literature to more general quantum states, and for any production mechanism. Finally, we argue that a CHSH violation measured in a collider is only a weak form of violation of Bell's theorem, necessarily containing a number of loopholes.
We investigate quantum coherence in the spin degrees of freedom of top--antitop pairs produced at the LHC using the l1-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 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 5σ in each region. In particular, in the intermediate-mass region, 400<Mttˉ<600GeV, we obtain Cl1=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±0.02, 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.
Abstract Entanglement is a central subject in quantum mechanics. Due to its genuine relativistic behavior and fundamental nature, high-energy colliders are attractive systems for the experimental study of fundamental aspects of quantum mechanics. We propose the detection of entanglement between the spins of top–antitop–quark pairs at the LHC, representing the first proposal of entanglement detection in a pair of quarks, and also the entanglement observation at the highest energy scale so far. We show that entanglement can be observed by direct measurement of the angular separation between the leptons arising from the decay of the top–antitop pair. The detection can be achieved with high statistical significance, using the current data recorded during Run 2 at the LHC. In addition, we develop a simple protocol for the quantum tomography of the top–antitop pair. This experimental technique reconstructs the quantum state of the system, providing a new experimental tool to test theoretical predictions. Our work explicitly implements canonical experimental techniques in quantum information in a two-qubit high-energy system, paving the way to use high-energy colliders to also study quantum information aspects.
Top and anti-top quark pair production at LHC provides a unique setting to probe non-classical correlations at the TeV scale. We study quantum information (QI) properties of the ttˉ spin state in pp collisions at s=13 TeV within the Standard Model Effective Field Theory (SMEFT), focusing on dimension-6 operators that induce anomalous chromo- and weak dipole moments of the top quark within their current experimental bounds. The ttˉ spin density matrix is reconstructed from the joint angular distribution of the final state charged leptons in the k-r-n helicity basis. We analyze three complementary QI quantities: concurrence-based quantum entanglement (QE), geometric quantum discord (GQD), and the Bell parameter,across four ttˉ invariant-mass bins. Within the Standard Model (SM), non-vanishing QE appears only near threshold (mttˉ≲400 GeV), while GQD remains nonzero across the full phase space, indicating persistent non-classical correlations even for separable states. Anomalous chromo-dipole interactions modify these observables primarily near threshold: μ^t induces asymmetric shifts, whereas d^t produces a mild symmetric response without Bell inequality violation. Among weak dipole operators, the CP-even coupling C2V generates the largest deformation of the QI observables, while ΔC1A,V leave them unchanged. These results demonstrate that QI observables derived from the ttˉ spin density matrix provide a complementary probe of anomalous top-quark interactions with distinct sensitivity to CP-even and CP-odd operator structures.
Quantum detection of CP violation in the ttˉ system: production
We investigate how possible new CP-violating top-quark interactions are encoded in the quantum state of a produced ttˉ pair. We derive analytic expressions for the production density matrix in several benchmark channels relevant to hadron, lepton and photon colliders. In a common spin basis, we identify two characteristic CP-odd structures in the Fano--Bloch decomposition: a difference between the top and antitop polarisation vectors and an antisymmetric component of the spin-correlation matrix. We construct observables that directly probe these structures and study how quantum information measures, including discord, concurrence, magic and trace distance, respond to CP-even and CP-odd SMEFT contributions. Finally, using current measurements and future collider projections, we assess the sensitivity of these observables to possible new sources of CP violation in top-quark production. This establishes the production-level framework whose experimental reconstruction is developed in a companion paper.
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 340GeV