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

TL;DR

This paper establishes explicit lower bounds on the entanglement needed for XOR non-local games, introducing a new algebraic technique that links near-optimal strategies to approximate representations of a C*-algebra.

Contribution

It presents a novel method for deriving entanglement lower bounds in XOR games using C*-algebra representations, extending Tsirelson's theorem.

Findings

Explicit XOR games requiring exponential entanglement

New technique relating strategies to C*-algebra representations

Extension of Tsirelson's theorem on quantum correlations

Abstract

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.