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arXiv · 0911.1525

Classical description of quantum randomness using stochastic gauge systems

Michel Feldmann
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Abstract

We present a classical probability model appropriate to the description of quantum randomness. This tool, that we have called stochastic gauge system, constitutes a contextual scheme in which the Kolmogorov probability space depends upon the experimental setup, in accordance with quantum mechanics. Therefore, the probability space behaves like a gauge parameter. We discuss the technical issues of this theory and apply the concept to classically emulate quantum entangled states and even `super-quantum' systems. We exhibit bipartite examples leading to maximum violation of Bell-CHSH inequalities like EPR pairs or exceeding the Tsirelson bound like PR-boxes, as well as tripartite cases simulating GHZ or W-states. We address also the question of partially correlated systems and multipartite entanglements. In this model, the classical equivalent of the entanglement entropy is identified with the Kullback-Leibler divergence. Hence, we propose a natural generalisation of this function to multipartite systems, leading to a simple evaluation of the degree of entanglement and determining the bounds of maximum entanglement. Finally, we obtain a constructive necessary and sufficient condition of multipartite entanglement.

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Michel Feldmann. 2010-05-31. Classical description of quantum randomness using stochastic gauge systems. https://arxiv.org/abs/0911.1525

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