State Determination and Sufficiency of Observables

Informational completeness and the possibility of state distinction and determination are among the more important issues of quantum statistics. We use spectral and semispectral (POV) measures to analyse these questions. For a given W ^?-algebra and a family of normal states on it we investigate the relation between sufficiency in Petz’s sense of a W ^?-subalgebra generated by a spectral measure, and the possibility of determination of these states by means of an observable.