Neumark Operators and Sharp Reconstructions, the finite dimensional case

Details Neumark Operators and Sharp Reconstructions, the finite dimensional case Neumark Operators and Sharp Reconstructions, the finite dimensional case

2010-05-17

arxiv.org/abs/1005.2955v1

Journal of Mathematical Physics, 48, 022102 (2007)

Physics

Mathematical Physics

37 pages

Scientific paper

10.1063/1.2437653

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.

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