Quantum instruments: II. Measurement theory

: Pellonpaa JP

Publisher: IOP PUBLISHING LTD

: 2013

: Journal of Physics A: Mathematical and Theoretical

: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

: J PHYS A-MATH THEOR

: ARTN 025303

: 2

: 46

: 2

: 15

: 1751-8113

DOI: https://doi.org/10.1088/1751-8113/46/2/025303

For any quantum observable (positive operator valued measure (POVM)), we show that its compatible quantum instruments can be identified with certain channels and can be seen as combinations of Luders operations and channels. We prove that a POVM is rank-1 exactly when its compatible instruments are nuclear and their associate channels are entanglement-breaking. Any instrument can be maximally refined into a rank-1 instrument. We present a characterization for (minimal) pure realizations of instruments and characterize completely the minimal pure measurement models of POVMs. The standard model of quantum measurement theory is generalized for arbitrary observables. Finally, we study post measurement states.