Perfect Embezzlement of Entanglement

Abstract

Van Dam and Hayden introduced a concept commonly referred to as embezzlement, where, for any entangled quantum state $\varphi$, there is an entangled catalyst state $\psi$, from which a high fidelity approximation of $\varphi \otimes \psi$ can be produced using only local operations. We investigate a version of this where the embezzlement is perfect (i.e., the fidelity is 1). We prove that perfect embezzlement is impossible in a tensor product framework, even with infinite-dimensional Hilbert spaces and infinite entanglement entropy. Then we prove that perfect embezzlement is possible in a commuting operator framework. We prove this using the theory of C*-algebras and we also provide an explicit construction. Next, we apply our results to analyze perfect versions of a nonlocal game introduced by Regev and Vidick. Finally, we analyze the structure of perfect embezzlement protocols in the commuting operator model, showing that they require infinite-dimensional Hilbert spaces.

27 pages, 9 figures

References in corpus (2)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Connes' embedding problem and Tsirelson's problem

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