A quantum system is represented by a Hilbert space and a measurement of the system is represented by a positive operator valued measure (POVM) from the σ-algebra of measurement events to the space of all bounded linear operators acting on the Hilbert space. In essence, a quantum measurement on a finite set is determined by positive semidefinite matrices that can viewed as matrix-valued probabilities. The linear span of these matrices is called an operator system. In this lecture I will explain how operator systems affiliated with quantum measurements can be used to characterise quantum measurements with a certain extremal property called cleanness.

Coauthors: Doug Farenick and Remus Floricel (University of Regina)