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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 $sqrt{n}$ (up to a logarithmic factor) 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.
In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We illustrate the
In this paper we introduce a simple and natural bipartite Bell scenario, by considering the correlations between two parties defined by general measurements in one party and dichotomic ones in the other. We show that unbounded Bell violations can be
For any finite number of parts, measurements and outcomes in a Bell scenario we estimate the probability of random $N$-qu$d$it pure states to substantially violate any Bell inequality with uniformly bounded coefficients. We prove that under some cond
Quantum entanglement plays a vital role in many quantum information and communication tasks. Entangled states of higher dimensional systems are of great interest due to the extended possibilities they provide. For example, they allow the realisation
We investigate the Bell inequalities derived from the graph states with violations detectable even with the presence of noises, which generalizes the idea of error-correcting Bell inequalities [Phys. Rev. Lett. 101, 080501 (2008)]. Firstly we constru