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Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU)

Entanglement in flavored scalar scattering

Enrico Maria Sessolo, Kamila Kowalska

Published Dec 9, 2025• 0 citations
Publisher

Abstract

We investigate quantum entanglement in high-energy $2\to 2$ scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the $S$-matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space.

DOI
10.22323/1.490.0113

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We compute the entanglement entropy variation between initial (separable or entangled in the momenta) and final states ΔSEΔS_EΔSE​ in an elastic scattering of a bipartite system composed by two interacting scalar particles. We perform a quantum field theoretical calculation to one loop order and verify that $ΔS_E $ changes as we vary the energy of incoming particles and the coupling strength in a non-trivial way.
Studies of scattering processes in scalar models with two Higgs doublets have recently hinted at a connection between the absence of flavor-space entanglement in Φ + Φ 0 scattering and an emergent SO(8) symmetry in the scalar potential. We extend the analysis to all scattering channels with two particles in the external states by treating the process as a four-qubit system in the weak isospin and flavor subspaces of the two-particle state. We work with a generic quantum-information-theoretic principle encoded by the commutativity of the initial-state density matrix with the transition matrix (at leading order in perturbation theory). This yields a special case of the entanglement minimization conditions previously derived in the literature, and we interpret the principle in terms of the conservation of nonstabilizerness (or “magic”). Working at leading order in the quartic couplings, we find a consistent set of conditions that implies an SO(8) symmetry on the quartic part of the potential for scattering an arbitrary initial state but a smaller SU ( 2 ) R symmetry when the initial state is chosen to have definite isospin. This follows by accounting for Bose symmetry in the initial state, which introduces entanglement between the isospin and flavor subspaces.