It is an established fact that entanglement is a resource. Sharing anentangled state leads to non-local correlations and to violations of Bellinequalities. Such non-local correlations illustrate the advantage of quantumresources over classical resources. Here, we study quantitatively Bellinequalities with $2\times n$ inputs. As found in [N. Gisin et al., Int. J. Q.Inf. 5, 525 (2007)] quantum mechanical correlations cannot reach the algebraicbound for such inequalities. In this paper, we uncover the heart of this effectwhich we call the {\it fraction of determinism}. We show that any quantumstatistics with two parties and $2 \times n$ inputs exhibits nonzero fractionof determinism, and we supply a quantitative bound for it. We then apply it toprovide an explicit {\it universal upper bound} for Bell inequalities with$2\times n$ inputs. As our main mathematical tool we introduce and prove a {\itreverse triangle inequality}, stating in a quantitative way that if some statesare far away from a given state, then their mixture is also. The inequality iscrucial in deriving the lower bound for the fraction of determinism, but isalso of interest on its own.
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