Quantum error correction on infinite-dimensional Hilbert spaces

Beny, Cedric, Kempf, Achim and Kribs, David W. (2009) Quantum error correction on infinite-dimensional Hilbert spaces. Journal of Mathematical Physics, 50 6: 062108-1-062108-24. doi:10.1063/1.3155783

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Author Beny, Cedric
Kempf, Achim
Kribs, David W.
Title Quantum error correction on infinite-dimensional Hilbert spaces
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
1527-2427
Publication date 2009-06
Sub-type Article (original research)
DOI 10.1063/1.3155783
Open Access Status File (Publisher version)
Volume 50
Issue 6
Start page 062108-1
End page 062108-24
Total pages 24
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Language eng
Abstract We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. We find that, under relatively mild conditions, much of the structure known from systems in finite-dimensional Hilbert spaces carries straightforwardly over to infinite dimensions. We also find that, at least in principle, there exist qualitatively new classes of quantum error correcting codes that have no finite-dimensional counterparts. We begin with a shift of focus from states to algebras of observables. Standard subspace codes and subsystem codes are seen as the special case of algebras of observables given by finite-dimensional von Neumann factors of type I. The new classes of codes that arise in infinite dimensions are shown to be characterized by von Neumann algebras of types II and III, for which we give in-principle physical examples.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Article # 062108

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Thu, 03 Sep 2009, 07:53:16 EST by Mr Andrew Martlew on behalf of Physics