Berry Schoenmakers, Jilles Tjoelker, Pim Tuyls, Evgeny A. Verbitskiy
Abstract
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We prove that the average smooth Renyi entropy rate will approach the entropy rate of a stationary, ergodic information source, which is equal to the Shannon entropy rate for a classical information source and the von Neumann entropy rate for a quantum information source.
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We prove that the average smooth Renyi entropy rate will approach the entropy rate of a stationary, ergodic information source, which is equal to the Shannon entropy rate for a classical information source and the von Neumann entropy rate for a quantum information source.
Key concepts: Von Neumann entropy, Ergodic theory, Entropy rate, Rényi entropy, Quantum relative entropy, Joint quantum entropy, Shannon's source coding theorem, Mathematics