A note on typicality in random quantum scattering

TL;DR

This paper investigates how random quantum scattering processes tend to disentangle a system's inner parts from its boundary, providing analytical and numerical insights into the typicality of such phenomena.

Contribution

It introduces a framework for analyzing typical entanglement behavior in quantum scattering with Haar-random unitaries, deriving formulas for average purity and fluctuation bounds.

Findings

Single scattering disentangles the inner system from the boundary.

Trace norm fluctuations are constrained by Levy's lemma.

Purity fluctuations decrease as environmental dimension increases.

Abstract

We consider scattering processes where a quantum system is comprised of an inner subsystem and of a boundary, and is subject to Haar-averaged random unitaries acting on the boundary-environment Hilbert space only. We show that, regardless of the initial state, a single scattering event will disentangle the unconditional state (i.e., the scattered state when no information about the applied unitary is available) across the inner subsystem-boundary partition. Also, we apply Levy's lemma to constrain the trace norm fluctuations around the unconditional state. Finally, we derive analytical formulae for the mean scattered purity for initial globally pure states, and provide one with numerical evidence of the reduction of fluctuations around such mean values with increasing environmental dimension.