Perfect embezzlement of entanglement
Van Dam and Hayden introduced the concept of approximate embezzlement of entanglement. Even if one allows infinite dimensional resource spaces but requires a bipartite tensor product structure of the resource space, perfect embezzlement is still impossible. But in the commuting operator framework perfect embezzlement is possible. We then introduce unitary correlation sets and relate these ideas to the conjectures of Connes and Tsirelson. Finally we show that a game of Regev and Vidick has no perfect strategy in a tensor product framework, even allowing infinite dimensional spaces, while it does in the commuting operator framework.
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