Crossing Symmetry and Entanglement

TL;DR

This paper explores how crossing symmetry in quantum field theories with $SU(N)$ symmetry influences entanglement in scattering processes, revealing that entanglement generation is inherent in such theories and can be understood through quantum gate operations.

Contribution

It recasts scattering amplitudes as quantum operations on internal states, showing that crossing symmetry induces recoupling relations and entanglement between channels.

Findings

Scattering amplitudes can be represented as quantum gates on internal states.

Crossing symmetry leads to recoupling relations among quantum gates.

Entanglement in one scattering channel implies entanglement in another.

Abstract

We study the interplay between crossing symmetry and entanglement in $2 \to 2$ scattering within local quantum field theories that possess an $SU(N)$ global symmetry. In particular, we recast scattering amplitudes of fixed helicity as quantum operations on the Hilbert space of internal quantum numbers, where the external states play the role of qudits. The entire space of $SU(N)$-invariant scattering operators between qudits is spanned by a minimal set of three quantum gates. Recoupling relations among quantum gates are shown to follow directly from the crossing properties of the underlying amplitudes and reveal that entanglement generated from separable states in one channel is necessarily intertwined with another. Consequently, we argue any interacting quantum field theory that realizes an $SU(N)$ global symmetry must generate entanglement in at least one scattering channel.