Commutative POVMs and Fuzzy Observables
S. Twareque Ali, Claudio Carmeli, Teiko Heinosaari, Alessandro Toigo
TL;DR
This paper reviews properties of fuzzy observables, focusing on commutative POVMs, and discusses their representations, fuzzification, and joint measurement aspects in quantum measurement theory.
Contribution
It introduces two representation theorems for commutative POVMs and elaborates on the concept of fuzzification and joint measurements.
Findings
Representation theorems for commutative POVMs in terms of PVMs
Detailed discussion on the notion of fuzzification
Observations on joint measurement procedures
Abstract
In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.
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