Operational measurements in quantum mechanics

Robert F. O’Connell, Daniel F. Walls

Masanao Ozawa

Piotr Kochański, Krzysztof Wódkiewicz

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.

Henry Margenau

Henry Margenau

K. Kong Wan, Robert H. Fountain, Z Y Tao

There has been a lot of interest in generalizing orthodox quantum mechanics to include POV measures as observables, namely as unsharp observables. Such POV measures are related to symmetric operators. The present paper examines how symmetric operators arise and how they can represent observables.