Lower bounds on the entanglement needed to play XOR non-local games

Details Lower bounds on the entanglement needed to play XOR non-local games Lower bounds on the entanglement needed to play XOR non-local games

2010-07-14

arxiv.org/abs/1007.2248v2

Physics

Quantum Physics

20 pages, no figures. Corrected abstract, body of paper unchanged

Scientific paper

We give an explicit family of XOR games with O(n)-bit questions requiring 2^n 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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