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When do pieces determine the whole? Extreme marginals of a completely positive map




TekijätHaapasalo E., Heinosaari T., Pellonpää J.

Julkaisuvuosi2014

JournalReviews in Mathematical Physics

Tietokannassa oleva lehden nimiReviews in Mathematical Physics

Vuosikerta26

Numero2

Sivujen määrä16

ISSN0129-055X

DOIhttps://doi.org/10.1142/S0129055X14500020

Verkko-osoitehttp://api.elsevier.com/content/abstract/scopus_id:84897636403


Tiivistelmä

We will consider completely positive maps defined on tensor products of von Neumann algebras and taking values in the algebra of bounded operators on a Hilbert space and particularly certain convex subsets of the set of such maps. We show that when one of the marginal maps of such a map is an extreme point, then the marginals uniquely determine the map. We will further prove that when both of the marginals are extreme, then the whole map is extreme. We show that this general result is the common source of several well-known results dealing with, e.g., jointly measurable observables. We also obtain new insight especially in the realm of quantum instruments and their marginal observables and channels. © 2014 World Scientific Publishing Company.



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