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Quantum Information Processing

, Volume 2, Issue 5, pp 381–419 | Cite as

Noiseless Subsystems and the Structure of the Commutant in Quantum Error Correction

  • John A. Holbrook
  • David W. Kribs
  • Raymond Laflamme
Article

Abstract

The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of this set of operators. This led to the discovery of noiseless subsystems. They are described by a set of operators obtained from the commutant of the noise generators. In this paper we derive a general method to compute the structure of this commutant in the case of unital noise.

PACS: 03.67.–a, 03.67.Pp

Quantum information quantum error correction noiseless subsystems decoherence 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • John A. Holbrook
    • 1
  • David W. Kribs
    • 1
    • 2
    • 3
  • Raymond Laflamme
    • 2
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada
  2. 2.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  3. 3.Perimeter Institute for Theoretical PhysicsNorth, WaterlooCanada

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