On the structure of covariant phase observables

We study the mathematical structure of covariant phase observables. Such observables can alternatively be expressed as phase matrices, as sequences of unit vectors, as sequences of phase states, or as equivalence classes of covariant trace-preserving operations. Covariant generalized operator measures are defined by structure matrices which form a W-*-algebra with phase matrices as its subset. The properties of the Radon-Nikodym derivatives of phase probability measures are studied. (C) 2002 American Institute of Physics.