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Bound Information: The Classical Analog to Bound Quantum Entanglement

Nicolas Gisin and Renato Renner and Stefan Wolf

It was recently pointed out that there is a close connection between information-theoretic key agreement and quantum entanglement purification. This suggests that the concept of bound entanglement (entanglement which cannot be purified) has a classical counterpart: bound information, which cannot be used to generate a secret key by any protocol. We analyze a probability distribution which results when a specific bound entangled quantum state is measured. We show strong evidence for the fact that the corresponding mutual information is indeed bound. The probable existence of such information contrasts previous beliefs in classical information theory.