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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 8: Quanten-Informationstheorie

MP 8.3: Talk

Thursday, March 6, 2008, 17:40–18:00, KGI-HS 1023

A Continuity Theorem for Stinespring's Dilation — Dennis Kretschmann^2,3, •Dirk-Michael Schlingemann^1,3, and Reinhard F. Werner³ — ¹ISI Foundation Torino, Quantum information theory unit, Italy — ²Quantum Information Theory Group, Dipartimento di Fisica A. Volta, Universita di Pavia, Italy — ³Institut f. Mathematische Physik, TU-Braunschweig, Germany

We report on our article [arXive:0710.2495] in which 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 also discuss applications to topics in quantum information theory, e.g., information-disturbance tradeoff and quantum bit commitment.