A Continuity Theorem for Stinespring's Dilation

2007/10/12 by Dennis Kretschmann, Kretschmann, Dennis, Dirk Schlingemann +3 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.0710.2495

openalex publication_date 2007/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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