Completely positive maps on modules, instruments, extremality problems, and applications to physics

Details Completely positive maps on modules, instruments, extremality problems, and applications to physics Completely positive maps on modules, instruments, extremality problems, and applications to physics

2012-02-27

arxiv.org/abs/1202.5905v1

Physics

Quantum Physics

32 pages

Scientific paper

Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we determine extreme quantum instruments, preparations, channels, and extreme autocorrelation functions. Various applications to quantum information and measurement theories are given. The structure of quantum instruments is analyzed thoroughly.

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