Interpolation problems by completely positive maps

Details Interpolation problems by completely positive maps Interpolation problems by completely positive maps

2010-12-08

arxiv.org/abs/1012.1675v1

Mathematics

Functional Analysis

Scientific paper

Given commuting families of Hermitian matrices {A1, ..., Ak} and {B1, ...., Bk}, conditions for the existence of a completely positive map L, such that L(Aj) = Bj for j = 1, ...,k, are studied. Additional properties such as unital or / and trace preserving on the map ? are also considered. Connections of the study to dilation theory, matrix inequalities, unitary orbits, and quantum information science are mentioned.

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