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The Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation

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3 Author(s)
Dennis Kretschmann ; Univ. of Cambridge, Cambridge ; Dirk Schlingemann ; Reinhard F. Werner

Stinespring's dilation theorem is the basic structure theorem for quantum channels: it states that any quantum channel arises from a unitary evolution on a larger system. Here we prove a continuity theorem for Stinespring's dilation: if two quantum channels are close in cb-norm, then it is always possible to find unitary implementations which are close in operator norm, with dimension-independent bounds. This result generalizes Uhlmann's theorem from states to channels and allows to derive a formulation of the information-disturbance tradeoff in terms of quantum channels, as well as a continuity estimate for the no-broadcasting theorem. We briefly discuss further implications for quantum cryptography, thermalization processes, and the black hole information loss puzzle.

Published in:

IEEE Transactions on Information Theory  (Volume:54 ,  Issue: 4 )