Information-theoretic interpretation of quantum formalism

Michel Feldmann

We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is merely construed as a technique of Bayesian inference for analyzing a logical system subject to classical constraints. This sole procedure leads to completely recover the standard quantum information theory and thus provides an information-theoretic rationale to its technical rules. In this framework, the great challenges of quantum mechanics become simple platitudes: Why is the theory probabilistic? Why is the theory linear? Where does the Hilbert space come from? In addition, most of the paradoxes, such as uncertainty principle, entanglement, contextuality, nonsignaling correlation, measurement problem, etc., become straightforwards features, while the amount of information conveyed by a wave vector is clarified. In the end, our major conclusion is that quantum information is nothing but classical information processed by Bayesian inference techniques and as such, consubstantial with Aristotelian logic.

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