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

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

2010-11-09

arxiv.org/abs/1011.2102v1

A slightly revised version has been published in J. Phys. A: Math. Theor. 44 (2011) 095307

Physics

Quantum Physics

11 pages, no figures

Scientific paper

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, $\pm1$-valued, stochastic processes. This bound is given by $\Vert C-\cos\Vert \geq(1-\frac{8}{\pi^{2}}) /\sqrt{2}\approx0.133\,95.$

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