Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order ω(√n/log²n) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative L_p embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.