A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
When do pieces determine the whole? Extreme marginals of a completely positive map
Tekijät: Haapasalo E., Heinosaari T., Pellonpää J.
Julkaisuvuosi: 2014
Journal: Reviews in Mathematical Physics
Tietokannassa oleva lehden nimi: Reviews in Mathematical Physics
Vuosikerta: 26
Numero: 2
Sivujen määrä: 16
ISSN: 0129-055X
DOI: https://doi.org/10.1142/S0129055X14500020
Verkko-osoite: http://api.elsevier.com/content/abstract/scopus_id:84897636403
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.
Ladattava julkaisu This is an electronic reprint of the original article. |