Modules and extremal completely positive maps

Modules and extremal completely positive maps Convex sets of completely positive maps and positive-(semi)definite kernels are considered in a very general context of modules over $$C^*$$ -algebras and a complete characterization of their (regular) extremal points is obtained. As a byproduct, we determine extremal autocorrelation functions. We present a generalization for the Choi isomorphism widely used in quantum information theory and generalize the concept of a completely positive quantum instrument. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Modules and extremal completely positive maps

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Publisher
Springer Basel
Copyright
Copyright © 2013 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0231-y
Publisher site
See Article on Publisher Site

Abstract

Convex sets of completely positive maps and positive-(semi)definite kernels are considered in a very general context of modules over $$C^*$$ -algebras and a complete characterization of their (regular) extremal points is obtained. As a byproduct, we determine extremal autocorrelation functions. We present a generalization for the Choi isomorphism widely used in quantum information theory and generalize the concept of a completely positive quantum instrument.

Journal

PositivitySpringer Journals

Published: Mar 22, 2013

References

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