  The concept of intrinsic and operational observables in quantum mechanics is
introduced. It is argued that, in any realistic description of a quantum
measurement that includes a detecting device, it is possible to construct from
the statistics of the recorded raw data a set of operational quantities that
correspond to the intrinsic quantum mechanical observable. Using the concept of
the propensity and the associated operational positive operator valued measure
(POVM) a general description of the operational algebra of quantum mechanical
observables is derived for a wide class of realistic detection schemes. This
general approach is illustrated by the example of an operational Malus
measurement of the spin phases and by an analysis of the operational homodyne
detection of the phase of an optical field with a squeezed vacuum in the unused
ports.
