A Continuity Theorem for Stinespring's Dilation

Dennis Kretschmann; Dirk Schlingemann; Reinhard F. Werner

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arXiv · 0710.2495

A Continuity Theorem for Stinespring's Dilation

Dennis Kretschmann·Dirk Schlingemann·Reinhard F. Werner

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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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BibTeX RIS

Dennis Kretschmann, Dirk Schlingemann, Reinhard F. Werner. 2007-10-12. A Continuity Theorem for Stinespring's Dilation. https://arxiv.org/abs/0710.2495

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