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arXiv:2601.09558

Quantum properties of heavy-fermion pairs at a lepton collider with polarised beams

Mohammad Mahdi Altakach, Priyanka Lamba, Fabio Maltoni, Kazuki Sakurai

hep-phhep-exhep-thquant-phSubmitted Jan 14, 2026• Announced Jan 15, 2026• 0 citations
v1 · Jan 14, 2026v2 · Jan 27, 2026
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Abstract

We investigate the quantum properties of heavy-fermion pairs, such as $t\bar t$ 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 $t\bar t$ 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.

Comments
46 pages, 23 figures, 5 tables

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We investigate the quantum properties of heavy-fermion pairs, such as ttˉt\bar tttˉ or τ+τ−τ^+τ^-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 ttˉt\bar tttˉ 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.
A bstract We investigate the quantum properties of heavy-fermion pairs, such as tt‾ t\overline{t} 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\overline{t} 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.
A bstract We study the quantum properties of top quark pairs in lepton colliders with unpolarised beams, including spin correlations, entanglement, and violation of Bell inequalities. We present analytical results in the SM and in the SMEFT and discuss several practical aspects, like the choice of quantisation axes and tt‾ t\overline{t} tt t t ¯ threshold effects. We also note a correspondence between parity symmetry and entanglement. We find that quantum observables exhibit a rich phenomenology in the SM, and can also provide additional leverage in detecting new physics residing at higher scales.
Quantum detection of CP violation in the ttˉt\bar{t}ttˉ system: production
We investigate how possible new CP-violating top-quark interactions are encoded in the quantum state of a produced ttˉt\bar tttˉ 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.
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Abstract The measurement of quantum entanglement can provide a new and most sensitive probe to physics beyond the Standard Model. We use the concurrence of the top-quark pair spin states produced at colliders to constrain the magnetic dipole term in the coupling between top quark and gluons, that of τ\tau τ τ -lepton pair spin states to bound contact interactions and that of τ\tau τ τ -lepton pairs or two-photons spin states from the decay of the Higgs boson in trying to distinguish between CP-even and odd couplings. These four examples show the power of the new approach as well as its limitations. We show that differences in the entanglement in the top-quark and τ\tau τ τ -lepton pair production cross sections can provide constraints better than those previously estimated from total cross sections or classical correlations. Instead, the final states in the decays of the Higgs boson remain maximally entangled even in the presence of CP-odd couplings and cannot be used to set bounds on new physics. We discuss the violation of Bell inequalities featured in all four processes.
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.