2008/11/04 by Cédric Bény, Achim Kempf, David W. Kribs · 21 citations
Computer Science · Physics and Astronomy · #Generalization #Hilbert space #Observable #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #SIC-POVM #Subspace topology #Von Neumann algebra #Von Neumann architecture #quant-ph
paper · pdf · doi:10.1063/1.3155783
published in Journal of Mathematical Physics 50(6) (American Institute of Physics)
arxiv created 2008/11/04 · openalex publication_date 2009/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.