In the framework of quantum computation, the fact that entangled states violate
Bell inequalities can be regarded as a positive statement: strategies using
entangled states perform better than classical strategies in non-local games.
But how does the performance of quantum strategies depend on the amount of
entanglement they have available? This is still a large open question.

I will explain how to determine the amount of entanglement required for optimal
strategies in XOR non-local games (a large class of non-local games which
includes the well-known CHSH inequality). The method uses an exact
characterization of optimal strategies, generalizing a result of Tsirelson from
1985. Since Tsirelson's result is often overlooked, I will show how Tsirelson's
result leads to examples of XOR games with n-bit questions requiring
exponential in n ebits to play optimally. I will also explain why Tsirelson's
result isn't sufficient to determine the amount of entanglement required for
all XOR games, and give some results for near-optimal strategies.