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Wigner-function description of EPR experiment

Riccardo Franco
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Abstract

We provide a detailed description of the EPR paradox (in the Bohm version) for a two qubit-state in the discrete Wigner function formalism. We compare the probability distributions for two qubit relevant to simultaneously-measurable observables (computed from the Wigner function) with the probability distributions representing two perfectly-correlated classic particles in a discrete phase-space. We write in both cases the updating formulae after a measure, thus obtaining a mathematical definition of \textit{classic collapse} and \textit{quantum collapse}. We study, with the EPR experiment, the joint probability distributions of Alice's and Bob's qubit before and after the measure, analyzing the non-local effects. In particular, we give a more precise definition of locality, which we call m-locality: we show that quantum systems may violate this kind of locality, thus preserving, in an EPR-like argument, the completeness of Quantum Mechanics.

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Riccardo Franco. 2007-01-12. Wigner-function description of EPR experiment. https://arxiv.org/abs/quant-ph/0701075

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