We investigate how possible new CP-violating top-quark interactions are encoded in the quantum state of a produced $t\bar t$ 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.
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.
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: tomography
We develop a quantum-tomographic framework for determining whether possible CP-odd effects in ttˉ events originate in production, in decay, or in both. In the narrow-width approximation, the process I→ttˉ→bℓ+νbˉℓ−νˉ factorises into a production density matrix and top and antitop decay density matrices. We extend the standard tomography procedure to a general anomalous Wtb vertex and derive the corresponding angular distributions. Polar-angle distributions retain their usual tomographic form, up to modifications of the spin-analysing powers, and can therefore be used to reconstruct the production density matrix and test its CP properties. By contrast, dedicated azimuthal observables involving the b--lepton decay planes contain characteristic sine modulations that provide linear probes of possible new CP-violating interactions in the decay vertex. Combining the two classes of observables gives a systematic strategy for separating sources of CP violation in production and in decay. We illustrate the resulting angular signatures for representative ttˉ production scenarios at hadron and lepton colliders.
We investigate the quantum properties of heavy-fermion pairs, such as ttˉ or τ+τ−, produced in lepton-lepton collisions with polarised beams. Focusing on spin correlations, entanglement, Bell-inequality violation, and quantum-information-theoretic measures such as purity and magic, we analyse how beam polarisation shapes the structure of the spin-density matrix. We derive analytic expressions for a wide range of helicity configurations, including both Standard Model contributions and generic new-physics effects parametrised by scalar, vector, and tensor four-fermion operators within an effective field theory framework. We show that beam polarisation unlocks a substantially richer set of spin configurations and significantly enhances sensitivity to non-standard interactions. As a phenomenological application, we study ttˉ production at a future linear collider and demonstrate that quantum observables provide a comprehensive and complementary probe of top-quark interactions and stronger constraints on the scale of new 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.
A bstract We investigate the quantum properties of heavy-fermion pairs, such as tt t t ¯ or τ + τ − , produced in lepton-lepton collisions with polarised beams. Focusing on spin correlations, entanglement, Bell-inequality violation, and quantum-information-theoretic measures such as purity and magic, we analyse how beam polarisation shapes the structure of the spin-density matrix. We derive analytic expressions for a wide range of helicity configurations, including both Standard Model contributions and generic new physics effects parametrised by scalar, vector, and tensor four-fermion operators within an effective field theory framework. We show that beam polarisation unlocks a substantially richer set of spin configurations and significantly enhances sensitivity to non-standard interactions. As a phenomenological application, we study tt t t ¯ production at a future linear collider and demonstrate that quantum observables provide a comprehensive and complementary probe of top-quark interactions and stronger constraints on the scale of new 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.