2009/11/08 by Michel Feldmann, M. Feldmann, Feldmann, Michel · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #General Physics (physics.gen-ph) #General Relativity and Quantum Cosmology (gr-qc) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #gr-qc #physics.gen-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.0911.1525
40 pages, 1 figure. Important corrections. Emphase on entanglement entropy and non-quantum systems
openalex publication_date 2009/11/08 · arxiv created 2010/05/31 · arxiv updated 2010/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.