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arXiv · 1606.05061

Perfect Embezzlement of Entanglement

Richard Cleve·Li Liu·Vern I. Paulsen
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Abstract

Van Dam and Hayden introduced a concept commonly referred to as embezzlement, where, for any entangled quantum state $\phi$, there is an entangled catalyst state $\psi$, from which a high fidelity approximation of $\phi \otimes \psi$ 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.

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Richard Cleve, Li Liu, Vern I. Paulsen. 2016-06-16. Perfect Embezzlement of Entanglement. https://doi.org/10.1063/1.4974818

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