Quantum instruments: I. Extreme instruments

: 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 025302

: 2

: 46

: 2

: 16

: 1751-8113

DOI: https://doi.org/10.1088/1751-8113/46/2/025302

The structure of completely positive quantum instruments is analyzed thoroughly. We characterize the extreme points of the convex set of instruments. The characterization holds also for nondiscrete instruments in infinite dimensions, and is applied to quantum observables, channels, and preparations which are special cases of instruments. We show that extreme instruments are discrete in finite dimensions.