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arXiv:2601.22212

Azimuthal angular entanglement between decaying particles in ultra-peripheral ion collisions

Spencer R. Klein

hep-phnucl-exnucl-thquant-phSubmitted Jan 29, 2026• Announced Jan 30, 2026
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Abstract

Ultra-peripheral collisions (UPCs) involving relativistic heavy ions are a unique laboratory to study quantum correlations. The intense electromagnetic fields generate high rates of photonuclear interactions, including events involving multiple photon exchange. Multiple photon exchange can result in the production of multiple vector mesons and/or nuclear excitations. These interactions share a common impact parameter, so the photons have the same linear polarization. The shared polarization entangles the particles, leading to unique quantum correlations. The decays of these vector excitations are sensitive to this polarization, allowing for the study of these correlations. This letter will compare classical and quantum calculations of the correlations between these azimuthal directions. The two approaches predict vert different angular correlations. The differences are akin to those seen with polarized photons in tests of Bells inequality. Uniquely, UPC photoproduction can produce final states containing three or more particles, all entangled with the same polarization. These more complex states exhibit additional unique phenomenology, allowing new tests of multi-particle entanglement.

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Ultra-peripheral collisions (UPCs) involving relativistic heavy ions are a unique laboratory to study quantum correlations. The intense electromagnetic fields generate high rates of photonuclear interactions, including events involving multiple photon exchange. Multiple photon exchange can result in the production of multiple vector mesons and/or nuclear excitations. These interactions share a common impact parameter, so the photons have the same linear polarization. The shared polarization entangles the particles, leading to unique quantum correlations. The decays of these vector excitations are sensitive to this polarization, allowing for the study of these correlations.
This letter will compare classical and quantum calculations of the correlations between these azimuthal directions. The two approaches predict vert different angular correlations. The differences are akin to those seen with polarized photons in tests of Bells inequality. Uniquely, UPC photoproduction can produce final states containing three or more particles, all entangled with the same polarization. These more complex states exhibit additional unique phenomenology, allowing new tests of multi-particle entanglement.
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The two-photon decay of highly charged hydrogenlike ions is studied within the framework of second-order perturbation theory, based on Dirac's equation. Attention has been paid to the angle-angle correlations between the two emitted photons. In particular, the density matrix theory is applied in order to explore how these angle-angle correlations are affected by the alignment of the excited states of the ions. Detailed computations have been carried out for the $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition in hydrogenlike uranium U91+{\mathrm{U}}^{91+}U91+ ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the 3d5∕23{d}_{5∕2}3d5∕2​ state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.
In quantum mechanics, quantum entanglement is a physical phenomenon in which quantum particles (such as photons, electrons...) are connected to each other despite the large distances between them.This phenomenon occurs when a pair or group of particles is created in such a way that the quantum state of a particular particle cannot be described independently of other particles, even if there is a large distance between these particles.This research dealt with a computerized theoretical study of John Bell's theory to verify quantum entanglement, which was later tested by the French scientist Alain Aspect on photons of light, and the polarization angles of light were (0.45, 22.5, 67.5)This experiment was conducted and the results were recorded from the virtual interactive quantum entanglement laboratory (VIQEL), which is highly efficient in simulating the equations of quantum mechanics and probability functions, where we obtained accurate results by increasing the number of photonic pairs involved in the experiment and then the results were compared with the results of previous research by other scientists to prove that the main variable, which is the angle of polarization, does not affect the result when its value changes, but its effect lies in the difference in angles in the experiment, which in turn enhances From the theory of quantum entanglement.
The study of entanglement in particle physics has been gathering pace in the past few years. It is a new field that is providing important results about the possibility of detecting entanglement and testing Bell inequality at colliders for final states as diverse as top-quark, τ-lepton pairs and Λ-baryons, massive gauge bosons and vector mesons. In this review, after presenting definitions, tools and basic results that are necessary for understanding these developments, we summarize the main findings—as published by the beginning of year 2024—including analyses of experimental data in B meson decays and top-quark pair production. We include a detailed discussion of the results for both qubit and qutrits systems, that is, final states containing spin one-half and spin one particles. Entanglement has also been proposed as a new tool to constrain new particles and fields beyond the Standard Model and we introduce the reader to this promising feature as well.
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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.