Qubit entanglement from forward scattering

TL;DR

This paper derives analytic expressions for the concurrence of the momentum-reduced final-state density matrix in relativistic $2\to 2$ scattering within perturbative $S$-matrix theory. It shows that, at leading order for a product initial state, the entanglement between two qubits is driven by the real part of the forward scattering amplitude, while the imaginary part governs momentum–qudit entanglement and contributes a subleading correction to the linearized entropy equal to the relative entropy of coherence. The authors verify an area-law relation for the linearized entropy and illustrate the formalism with two phenomenological cases: high-energy scalar scattering in the 2HDM and high-energy $e^+e^-$ annihilation in QED, highlighting how forward amplitudes control entanglement across models. The results offer a principled link between amplitude structure and post-scattering entanglement and suggest avenues for exploring emergent symmetries through entanglement extremization and extensions to richer Hilbert-space partitions.

Abstract

In the context of entanglement in relativistic $2\to 2$ scattering described by a perturbative $S$-matrix, we derive analytically the concurrence for a mixed final state of two qubits corresponding to a discrete quantum number of the scattered particles. Given an initial product state, the derived concurrence depends at the leading order on the real part of the inelastic forward amplitude and the initial state only. We also point out that the real part of the forward amplitude provides a subleading correction to the linearized entropy, reducing it by an amount that, for a computational-basis state, is equivalent to the relative entropy of coherence. We illustrate our findings with two examples of phenomenological interest: high-energy scattering of two scalar fields in the two-Higgs doublet model, and high-energy electron-positron annihilation.