Interpolation by completely positive maps
Chi-Kwong Li, Yiu‐Tung Poon · Linear and Multilinear Algebra · 2011
Given commuting families of Hermitian matrices {A 1, … , A k } and {B 1, … , B k }, conditions for the existence of a completely positive map Φ, such that Φ(A j ) = B j for j = 1, … , k, are studied. Additional properties such as unital or/and trace preserving on the map Φ are also considered. Connections of the study to dilation theory, matrix inequalities, unitary orbits and quantum information science are mentioned.