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

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...

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Bibliographic Details
Published in:IEEE transactions on information theory 2008-04, Vol.54 (4), p.1708-1717
Main Authors: Kretschmann, D., Schlingemann, D., Werner, R.F.
Format: Article
Language:English
Subjects:
Applied sciences
Classical and quantum physics: mechanics and fields
Cryptography
Electronics
Exact sciences and technology
Hilbert space
Information science
Information theory
Information, signal and communications theory
information-disturbance tradeoff
Intersymbol interference
Mathematics
Physics
Purification
Quantum channels
Quantum cryptography
Quantum information
Quantum mechanics
Signal and communications theory
State estimation
Stinespring dilation
Telecommunications and information theory
Theorems
Tradeoff analysis
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2008.917696