Lower bound for the mean square distance between classical and quantum spin correlations

Abstract

Bell's theorem prevents local Kolmogorov-simulations of the singlet state of two spin-1/2 particles. We derive a positive lower bound for the $L^2$-distance between the quantum mechanical spin singlet anticorrelation function $\cos$ and any of its classical approximants $C$ formed by the stationary autocorrelation functions of mean-square-continuous, $2\pi$-periodic, $\pm 1$-valued, stochastic processes. This bound is given by $\Vert C-\cos \Vert \ge (1-\frac{8}{{\pi }^2})/\sqrt{2}\approx 0.13395.$

11 pages, no figures