Lower bounds on the entanglement needed to play XOR non-local games
Abstract
We give an explicit family of XOR games with O(n)-bit questions requiring 2n ebits to play near-optimally. More generally we introduce a new technique for proving lower bounds on the amount of entanglement required by an XOR game: we show that near-optimal strategies for an XOR game G correspond to approximate representations of a certain C*-algebra associated to G. Our results extend an earlier theorem of Tsirelson characterising the set of quantum strategies which implement extremal quantum correlations.
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