Structural change in multipartite entanglement sharing: a random matrix approach

TL;DR

This paper investigates how multipartite entanglement sharing in a system with two qubit environments and a shuttling ancilla changes under random initial states, revealing invariant properties and abrupt structural transitions.

Contribution

It introduces a random matrix approach to analyze typical entanglement properties and identifies conditions for abrupt changes in entanglement structure.

Findings

Average entanglement remains constant under Heisenberg interaction.

Entanglement-sharing structure can undergo abrupt modifications.

Results are invariant to initial environmental state randomness.

Abstract

We study the typical entanglement properties of a system comprising two independent qubit environments interacting via a shuttling ancilla. The initial preparation of the environments is modeled using random-matrix techniques. The entanglement measure used in our study is then averaged over many histories of randomly prepared environmental states. Under a Heisenberg interaction model, the average entanglement between the ancilla and one of the environments remains constant, regardless of the preparation of the latter and the details of the interaction. We also show that, upon suitable kinematic and dynamical changes in the ancilla-environment subsystems, the entanglement-sharing structure undergoes abrupt modifications associated with a change in the multipartite entanglement class of the overall system's state. These results are invariant with respect to the randomized initial state of the environments.