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arXiv · 1011.2102

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

Gebhard Gruebl·Lukas Wurzer
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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, $\pm1$-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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Gebhard Gruebl, Lukas Wurzer. 2010-11-09. Lower bound for the mean square distance between classical and quantum spin correlations. https://doi.org/10.1088/1751-8113/44/9/095307

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