Information-theoretic interpretation of quantum formalism

Abstract

We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and free of any additional axiom or principle. Quantum information is merely construed as a technique of statistical estimation for analyzing a logical system subject to classical constraints, regardless of the specific variables used. The problem is initially formulated in a standard Boolean algebra involving a particular set of working variables. Statistical estimation is to express the truth table in terms of likelihood probability instead of the variables themselves. The constraints are thus converted into a Bayesian prior. This method leads to solving a linear programming problem in a real-valued probability space. The complete set of alternative Boolean variables is introduced afterwards by transcribing the probability space into a Hilbert space, thanks to Gleason's theorem. This allows to completely recover standard quantum information and provides an information-theoretic rationale to its technical rules. The model offers a natural answer to the major puzzles that base quantum mechanics: Why is the theory linear? Why is the theory probabilistic? Where does the Hilbert space come from? Also, most of the paradoxes, such as entanglement, contextuality, nonsignaling correlation, measurement problem, etc., find a quite trivial explanation, while the concept of information conveyed by a wave vector is clarified. We conclude that quantum information, although dramatically expanding the scope of classical information, is not different from the information itself and is therefore a universal tool of reasoning.