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-squarecontinuous, 2π-periodic, ±1-valued, stochastic processes. This bound is given by C − cos ≥ 1 − 8 π 2 / √ 2 ≈ 0.133 95.