dorsal/arxiv
View SchemaThe Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation
| Authors | Dennis Kretschmann, Dirk Schlingemann, Reinhard F. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605009 |
| URL | https://arxiv.org/abs/quant-ph/0605009 |
Abstract
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.
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"abstract": "Stinespring\u0027s dilation theorem is the basic structure theorem for quantum\nchannels: it states that any quantum channel arises from a unitary evolution on\na larger system. Here we prove a continuity theorem for Stinespring\u0027s dilation:\nif two quantum channels are close in cb-norm, then it is always possible to\nfind unitary implementations which are close in operator norm, with\ndimension-independent bounds. This result generalizes Uhlmann\u0027s theorem from\nstates to channels and allows to derive a formulation of the\ninformation-disturbance tradeoff in terms of quantum channels, as well as a\ncontinuity estimate for the no-broadcasting theorem. We briefly discuss further\nimplications for quantum cryptography, thermalization processes, and the black\nhole information loss puzzle.",
"arxiv_id": "quant-ph/0605009",
"authors": [
"Dennis Kretschmann",
"Dirk Schlingemann",
"Reinhard F. Werner"
],
"categories": [
"quant-ph"
],
"title": "The Information-Disturbance Tradeoff and the Continuity of Stinespring\u0027s Representation",
"url": "https://arxiv.org/abs/quant-ph/0605009"
},
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