A1 Refereed original research article in a scientific journal
Quantum instruments: II. Measurement theory
Authors: Pellonpaa JP
Publisher: IOP PUBLISHING LTD
Publication year: 2013
Journal: Journal of Physics A: Mathematical and Theoretical
Journal name in source: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Journal acronym: J PHYS A-MATH THEOR
Article number: ARTN 025303
Number in series: 2
Volume: 46
Issue: 2
Number of pages: 15
ISSN: 1751-8113
DOI: https://doi.org/10.1088/1751-8113/46/2/025303
Abstract
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.
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.
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