Li Liu

Entanglement of embezzlement is the process of converting a separable state to an entangled state using only local operations with the help of a large catalyst state. It defies naive intuitions about entanglement as a static resource and demonstrates the subtleties of infinite-dimensional systems. There has been recent studies on approximate embezzlement protocols. This work combines two results regarding exact embezzlement. The first result is explicit protocols for universal embezzlement covering both approximate and exact cases using simple algebraic tools. In the exact case, we achieved the first known exact universal embezzlement protocol. The second result is a self-testing-like property about the structural requirement for the catalyst for embezzlement. In particular, we showed that for a catalyst to embezzle a state exactly, it must contain infinite copies of the embezzled state. This work uses C*-algebra as a model for non-local systems in infinite dimensions instead of the standard commuting operator in Hilbert space model or the von Neumann algebraic model to provide a clean and simple proofs for the resutls.