A continuity theorem for Stinespring’s dilation

We show a continuity theorem for Stinespring’s dilation: two completely positive maps between arbitrary C∗-algebras are close in cb-norm if and only if we can find corresponding dilations that are close in operator norm. The proof establishes the equivalence of the cb-norm distance and the Bures distance for completely positive maps. We briefly discuss applications to quantum information theory. © 2008 Elsevier Inc. All rights reserved