Extended nonlocal games from quantum-classical
Vincent Russo, IQC
Several variants of nonlocal games have been considered in the study of quantum entanglement and nonlocality. In this talk, we shall consider two such variants called quantum-classical games and extended nonlocal games. The players, Alice and Bob, may play the game according to various classes of strategies. An entangled strategy is one in which Alice and Bob use quantum resources in the form of a shared quantum state and sets of measurements. One may ask whether the dimension of the shared state makes a difference in how well the players can perform using an entangled strategy. We show that there does exist extended nonlocal games for which no finite-dimensional entangled strategy can be optimal. This builds off of previous work that answered a similar question for quantum-classical games. The same question for nonlocal games remains open and is related to the Connes Embedding Conjecture. Extended nonlocal games are also equivalent to a particular type of steering; which is a concept initially thought of by Schrödinger. Our result implies the existence of a tripartite steering inequality for which an infinite-dimensional quantum state is required in order to achieve a maximal violation.
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