Neumark Operators and Sharp Reconstructions, the finite dimensional case

Original · EN

A commutative POV measure F with real spectrum is characterized by the existence of a PV measure E (the sharp reconstruction of F) with real spectrum such that F can be interpreted as a randomization of E. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark's extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of F and the sharp reconstruction of F. The relevance of this result to the theory of non-ideal quantum measurement and to the definition of unsharpness is analyzed.