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Conditions for the Approximate Correction of Algebras

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Theory of Quantum Computation, Communication, and Cryptography (TQC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5906))

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Abstract

We study the approximate correctability of general algebras of observables, which represent hybrid quantum-classical information. This includes approximate quantum error correcting codes and subsystems codes. We show that the main result of [1] yields a natural generalization of the Knill-Laflamme conditions in the form of a dimension independent estimate of the optimal reconstruction error for a given encoding, measured using the trace-norm distance to a noiseless channel.

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Author information

Authors and Affiliations

  1. Centre for Quantum Technologies, National University of Singapore,  

    Cédric Bény

Authors
  1. Cédric Bény
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Editor information

Editors and Affiliations

  1. Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, ON, Canada

    Andrew Childs

  2. Institute for Quantum Computing, University of Waterloo, N2L 3G1, Waterloo, Canada

    Michele Mosca

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© 2009 Springer-Verlag Berlin Heidelberg

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Bény, C. (2009). Conditions for the Approximate Correction of Algebras. In: Childs, A., Mosca, M. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2009. Lecture Notes in Computer Science, vol 5906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10698-9_7

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  • DOI: https://doi.org/10.1007/978-3-642-10698-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10697-2

  • Online ISBN: 978-3-642-10698-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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