The silence of binary Kerr

TL;DR

This paper investigates the entanglement properties of scattering processes involving spinning particles, finding that minimal coupling, akin to classical Kerr black holes, produces nearly zero entanglement entropy, unlike non-minimal couplings.

Contribution

It demonstrates that scattering of classical Kerr black holes results in negligible entanglement, highlighting a unique feature of minimal gravitational couplings in quantum scattering.

Findings

Minimal coupling yields near-zero entanglement entropy.

Non-vanishing spin multipole moments increase entanglement.

Entanglement entropy difference is nearly zero for Kerr-like scattering.

Abstract

A non-trivial $\mathcal{S}$-matrix generally implies a production of entanglement: starting with an incoming pure state the scattering generally returns an outgoing state with non-vanishing entanglement entropy. It is then interesting to ask if there exists a non-trivial $\mathcal{S}$-matrix that generates no entanglement. In this letter, we argue that the answer is the scattering of classical black holes. We study the spin-entanglement in the scattering of arbitrary spinning particles. Augmented with Thomas-Wigner rotation factors, we derive the entanglement entropy from the gravitational induced $2\rightarrow 2$ amplitude. In the Eikonal limit, we find that the relative entanglement entropy, defined here as the \textit{difference} between the entanglement entropy of the \textit{in} and \textit{out}-states, is nearly zero for minimal coupling irrespective of the \textit{in}-state, and increases significantly for any non-vanishing spin multipole moments. This suggests that minimal couplings of spinning particles, whose classical limit corresponds to Kerr black hole, has the unique feature of generating near zero entanglement.