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arXiv:2609.14700

Spin-spin entanglement at high energy

Michael Fucilla, Yoshitaka Hatta, Bo-Wen Xiao

hep-phquant-phSubmitted Sep 13, 2026• Announced Sep 15, 2026
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Abstract

Spin correlations offer a quantum-information perspective on the partonic final states produced in high-energy scattering. We discuss the spin-density matrix of a heavy quark-antiquark pair in two complementary small-$x$ processes. In coherent diffractive production, color-singlet exchange enforces an unusually strong relation between entanglement and Bell nonlocality: a longitudinal photon creates a maximally entangled pair, whereas for a transverse photon the pair is generically both entangled and Bell nonlocal, with a model-independent point of maximal entanglement. In inclusive back-to-back production, the density matrix factorizes into a hard spin tensor and the unpolarized and linearly polarized Weizsäcker--Williams gluon distributions. The latter generates an azimuthal modulation and can increase the concurrence when the dijet relative momentum and imbalance are approximately orthogonal. Strikingly, in the saturation model considered, nonlinear effects wash out this modulation for $q_\perp\lesssim 3Q_s$, whereas the dilute BFKL limit, in which $G_2/G_0\to1$, yields a maximal modulation independent of the imbalance magnitude. These results connect quantum-information observables with the Pomeron and saturation physics.

Comments
7 pages, 2 figures. Proceedings of the 33rd International Workshop on Deep Inelastic Scattering and Related Subjects (DIS2026), 4-8 May 2026, Bologna, Italy

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Spin correlations offer a quantum-information perspective on the partonic final states produced in high-energy scattering. We discuss the spin-density matrix of a heavy quark-antiquark pair in two complementary small-xxx processes. In coherent diffractive production, color-singlet exchange enforces an unusually strong relation between entanglement and Bell nonlocality: a longitudinal photon creates a maximally entangled pair, whereas for a transverse photon the pair is generically both entangled and Bell nonlocal, with a model-independent point of maximal entanglement. In inclusive back-to-back production, the density matrix factorizes into a hard spin tensor and the unpolarized and linearly polarized Weizsäcker--Williams gluon distributions. The latter generates an azimuthal modulation and can increase the concurrence when the dijet relative momentum and imbalance are approximately orthogonal. Strikingly, in the saturation model considered, nonlinear effects wash out this modulation for q⊥≲3Qsq_\perp\lesssim 3Q_sq⊥​≲3Qs​, whereas the dilute BFKL limit, in which G2/G0→1G_2/G_0\to1G2​/G0​→1, yields a maximal modulation independent of the imbalance magnitude. These results connect quantum-information observables with the Pomeron and saturation physics.
Within the collinear factorization framework based on Generalized Parton Distributions (GPDs), we calculate the spin density matrix of exclusively produced quark and antiquark pairs uuˉu\bar{u}uuˉ, ddˉd\bar{d}ddˉ, ssˉs\bar{s}ssˉ, ccˉc\bar{c}ccˉ, bbˉb\bar{b}bbˉ in electron-proton scattering. The presence of both real and imaginary parts in the scattering amplitudes leads to a rich pattern of entanglement between the quark and the antiquark. We map out kinematical regions where the pairs exhibit entanglement, Bell nonlocality and non-stabilizerness (`magic'). We also predict that massive quarks and antiquarks are transversely polarized, similar to the well-known transverse hyperon polarization in unpolarized collisions. In strangeness, charm and bottom productions, the polarization can reach 50-80\% in certain kinematic regions in the low-energy runs of the Electron-Ion Collider.
Using the soft-gluon theorem, we identify a soft-recoil mechanism by which unresolved gluon radiation induces decoherence in the spin correlations of heavy quark-antiquark pairs produced by longitudinally polarized virtual photons in deep-inelastic scattering. Upon tracing over the unresolved gluon, the reduced spin density matrix is block diagonal in the mirror parity of the production plane and is governed by two coefficients: a parity-odd normal-spin flip, which reduces the normal-axis correlation, and a parity-even stochastic rotation of the spin-correlation plane about its normal, which suppresses the in-plane spin coherences while leaving the normal-axis correlation unchanged. From the complete tree-level next-to-soft amplitude with the exact color-octet structure we derive both coefficients, together with the trace and antisymmetric in-plane terms, in closed form. The parity-odd coefficient is the larger one, by a factor of at least 3.53.53.5, and grows as the inverse square of the heavy-quark transverse momentum. We estimate the resulting reduction of concurrence and Bell-CHSH violation, and propose an infrared-safe, radiation-binned EIC observable, formed at fixed Born kinematics after longitudinal-transverse separation, which isolates the two channels. We estimate its size, including multiple wide-angle emissions in an independent-emission model, the conditions under which detector and kinematic effects cancel, and the statistics required. The latter, however, exceed the yield of exclusive heavy-baryon pairs at nominal EIC luminosity by several orders of magnitude, makes the observable elusive for the measurement accessible in that channel.
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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.
Spin Correlation and Quantum Entanglement of Fermion Pairs in Transversely Polarized e−e+e^-e^+e−e+ Collisions
We systematically study the spin correlations and quantum entanglement in transversely polarized electron-positron collisions. We find that the sss-channel QED process e−e+→ffˉe^-e^+\to f\bar fe−e+→ffˉ​ produces a maximally entangled state in the entire phase space when the initial beams are transversely polarized, while the quantum magic varies in different phase space points for the maximally entangled Bell states. For electroweak processes, the spin configuration of final states depends on chiral couplings, and the entanglement is also greatly enhanced by transverse polarization as in the QED process. For Bhabha scattering with additional ttt-channel contributions, the transverse polarization still increases the final state entanglement, although with some dilution. The sensitive dependence of final spin states on the transverse polarization makes the beam polarization a powerful tool for generating and controlling quantum entanglement in collider experiments, opening up new opportunities for quantum information studies at high-energy colliders.
A bstract A photon linear collider, the two-photon collision mode of an e + e − linear collider, uses high-energy laser photons backscattered off the incoming electrons and positrons. The colliding-photon polarization is fully controllable through the polarizations of the initial electron and positron beams and laser photons. We investigate the impact of colliding-photon polarization on the observability of quantum entanglement in top-quark pair production at a photon linear collider. Constructing the spin density matrix of the tt‾t\overline{t }tt two-qubit system from the helicity amplitudes, we demonstrate that a photon linear collider is an ideal machine to probe quantum entanglement and Bell nonlocality across the broad phase space of the process.