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Title: Quantum error correction on infinite-dimensional Hilbert spaces
Authors: B́ny, C. 
Kempf, A.
Kribs, D.W.
Issue Date: 2009
Citation: B́ny, C., Kempf, A., Kribs, D.W. (2009). Quantum error correction on infinite-dimensional Hilbert spaces. Journal of Mathematical Physics 50 (6) : -. ScholarBank@NUS Repository.
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. © 2009 American Institute of Physics.
Source Title: Journal of Mathematical Physics
ISSN: 00222488
DOI: 10.1063/1.3155783
Appears in Collections:Staff Publications

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