The Applicability of Shannon Information in Quantum Mechanics and Zeilinger's Foundational Principle

Recently, Brukner and Zeilinger have presented a number of arguments suggesting that the Shannon information is not well defined as a measure of information in quantum mechanics. If established, this result would be highly significant, as the Shannon information is fundamental to the way we think about information not only in classical but also in quantum information theory. On consideration, however, these arguments are found unsuccessful; I go on to suggest how they might be arising as a consequence of Zeilinger`s proposed foundational principle for quantum mechanics.