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.
@article{arxiv.1007.2248,
title = {Lower bounds on the entanglement needed to play XOR non-local games},
author = {William Slofstra},
journal= {arXiv preprint arXiv:1007.2248},
year = {2015}
}
Comments
20 pages, no figures. Corrected abstract, body of paper unchanged