Mutually exclusive and exhaustive quantum states

The identification of a set of mutually exclusive and exhaustive propositions concerning the states of quantum systems is a corner stone of the information-theoretic foundations of quantum statistics; but the set which is conventionally adopted is in fact incomplete, and is customarily deduced from numerous misconceptions of basic quantum mechanical principles. This paper exposes and corrects these common misstatements. It then identifies a new set of quantum state propositions which is truly exhaustive and mutually exclusive, and which is compatible with the foundations of quantum theory.

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