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arXiv:2604.10136 · Physical review. D/Physical review. D.

Characterizing entanglement dynamics in QED scattering processes

Massimo Blasone, Silvio De Siena, Gaetano Lambiase, Bruno Micciola, Kyrylo Simonov

quant-phhep-phSubmitted Apr 11, 2026• Announced Apr 14, 2026• 0 citations• Revised Jul 26, 2026 (v2)
v1 · Apr 11, 2026v2 · Jul 26, 2026
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Abstract

We study entanglement dynamics among helicity degrees of freedom in quantum electrodynamics (QED) scattering processes. For generic initial states, we consider scattering at fixed momentum, corresponding to a generalized measurement described by a positive operator-valued measure, resulting in a post-measurement state. Such processes are modeled in terms of quantum maps, whose spectral structure fully determines the associated entanglement dynamics. For scattering involving fermions only, maximal entanglement present in the initial state is always preserved. Moreover, iterating the corresponding quantum maps on arbitrary initial states, we obtain the fixed points of the maps, which, in the largest number of cases, are asymptotic (pure) maximally entangled states. The structure of the maps also accounts for the entanglement dynamics in processes involving both fermions and photons. The defining properties of these maps originate from discrete symmetries of the QED interaction.

Comments
8 pages, 4 figures, revised version. Partially overlaps with arXiv:2505.06878

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We investigate the properties of quantum electrodynamics (QED) two-particle scattering processes when an arbitrarily sharp filtering of the outgoing particles in momentum space is performed. We find that these processes are described by dynamical quantum maps, whose structure is such that any initial state is transformed into a maximally entangled state, after an infinite number of iterations of the map. This structural property is exactly realized if all the colliding particles are massive fermions while, when photons are involved, it is verified in a partial way, depending on the process under consideration.
We reformulate the phenomenon of maximal entanglement conservation in Quantum Electrodynamics (QED) scattering processes, previously discussed in earlier works, using the tools of quantum maps and invariant sets. These sets are characterized as hypersurfaces within the six-dimensional parameter space. Furthermore, we speculate over a possible irreversible (ever-increasing) behavior of entanglement in QED scatterings. • Complete transfer of maximal entanglement in Bhabha scattering. • QED scattering processes preserve maximal entanglement for fermionic systems. • We present the invariant sets representing the conserved maximally entangled states. • Preliminary studies suggest a global rise in entanglement in QED interactions. • Future work will address mixed states and all particle d.o.f.
We study the behavior of entanglement between different degrees of freedom of scattering fermions, based on an exemplary QED scattering process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. The variation of entanglement entropy between two fermions from an initial state to the final state was computed, with respect to different entanglement between the ingoing particles. This variation of entanglement entropy is found to be proportional to an area quantity, the total cross section. We also study the spin-momentum and helicity-momentum entanglements within one particle in the aforementioned scattering process. The calculations of the relevant variations of mutual information in the same inertial frame reveals that, for a maximally entangled initial state, the scattering between the particles does not affect the degree of both of these entanglements of one particle in the final state. It is also found that the increasing degree of entanglement between two ingoing particles would restrict the generation of entanglement between spin (helicity) and momentum of one outgoing particle. And the entanglement between spin and momentum within one particle in the final state is shown to always be stronger than that for helicity-momentum for a general initial entanglement state, implying significantly distinct properties of entanglement for the helicity and spin perceived by an inertial observer.
We exploit the complete complementarity relations (CCR) to fully characterize various aspects of quantumness in quantum electrodynamics (QED) scattering processes at tree level. As a paradigmatic example, we consider Bhabha scattering in two different configurations: in the first case, the initial state is factorized in the spin and we study the generation of entanglement due to the scattering. Then we consider the most general case in which the initial state can be entangled: we find that the scattering generates and distributes quantum information in a nontrivial way among the spin degrees of freedom of the particles, with CCR relations being preserved. An important outcome of our analysis is that maximal entanglement is conserved in the scattering process involving only fermions as input and output states, with a more complex situation if photons are present.
We study two-body scattering as an SU(N)-equivariant map acting on tensor-product representation spaces and analyze the entanglement generated by the SSS-matrix. This representation-theoretic perspective separates group structure from dynamics: the decomposition of R ⁣⊗ ⁣R′R\!\otimes\!R'R⊗R′ fixes the invariant operator algebra and therefore the qualitative entangling power of the process. For particles in the fundamental representation, EndSU(N)(N ⁣⊗ ⁣N)=Span{I,S}\mathrm{End}_{\mathrm{SU}(N)}(N\!\otimes\!N)=\mathrm{Span}\{\mathbb{I},\mathbb{S}\}EndSU(N)​(N⊗N)=Span{I,S}, so only the identity and swap directions preserve separability, whereas generic combinations generate entanglement. Adjoint-adjoint scattering involves a larger invariant algebra involving ddd-tensors and is intrinsically entangling. In Yang-Mills theory one can use color-kinematics duality to show that the color kernel lies on a fixed ray of this operator space, yielding a universal maximum of the outgoing entanglement for scattering at right angles, E⋆(2)=34E_\star^{(2)}=\tfrac{3}{4}E⋆(2)​=43​ for SU(2)SU(2)SU(2) and E⋆(3)≃0.91E_\star^{(3)}\simeq0.91E⋆(3)​≃0.91, independent of kinematics. Dimension-six operators preserve this universality, while dimension-eight deformations populate new color sectors and shift E⋆(N)E_\star^{(N)}E⋆(N)​, suggesting that entanglement in color space functions as a tomographic probe of effective operators. In helicity space, requiring maximally entangled inputs to scatter into maximally entangled outputs uniquely selects the Yang-Mills quartic coupling and enforces the color Jacobi identity, restating the on-shell Ward constraints as conditions on entanglement preservation. Our results suggest that the information-theoretic viewpoint unifies algebraic, geometric, and dynamical aspects of scattering.
We study real-time meson-meson scattering processes in (1+1)(1+1)(1+1)-dimensional QED by means of Tensor Networks. We prepare initial meson wave packets with given momentum and position, starting from the free fermions model and extending it to the interaction theory. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we measure the scattering amplitudes for the process in terms of the initial and final momenta and the entanglement produced by the collision. We remarkably find two different regimes for the asymptotic entanglement between the two mesons: it is perturbatively small for weak couplings, while, in the intermediate regime, it turns out to reach a non-zero value at long times after the scattering.