A Continuity Theorem for Stinespring's Dilation

Understand

We show a continuity theorem for Stinespring's dilation: two completely positive maps between arbitrary C*-algebras are close in cb-norm iff 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.