2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139930We 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.18 pages, no figuresQuantum PhysicsMathematical PhysicsOperator Algebrastext