Embezzlement as a "Self-Test" for Infinite Copies of Entangled States
Abstract
We investigate the operator-algebraic structure underlying entanglement embezzlement, a phenomenon where a fixed entangled state (the catalyst) can be used to generate arbitrary target entangled states without being consumed. We show that the ability to embezzle a target state imposes strong internal constraints on the catalyst state : specifically, must contain infinitely many mutually commuting, locally structured copies of . This property is formalized using C*-algebraic tools and is analogous to a form of self-testing, certifying the presence of infinite copies of within . Using this infinite-copy certification. Our results clarify the structural requirements for embezzlement and provide new conceptual tools for analyzing state certification in infinite-dimensional quantum systems.
Cite
@article{arxiv.2509.05036,
title = {Embezzlement as a "Self-Test" for Infinite Copies of Entangled States},
author = {Li Liu},
journal= {arXiv preprint arXiv:2509.05036},
year = {2026}
}