Quantum error-correcting subsystems are unitarily recoverable subsystems

David W. Kribs and Robert W. Spekkens
Phys. Rev. A 74, 042329 – Published 25 October 2006

Abstract

We show that every correctable subsystem for an arbitrary noise operation can be recovered by a unitary operation, where the notion of recovery is more relaxed than the notion of correction insofar as it does not protect the subsystem from subsequent iterations of the noise. We also demonstrate that in the case of unital noise operations one can identify a subset of all correctable subsystems—those that can be corrected by a single unitary operation—as the noiseless subsystems for the composition of the noise operation with its dual. Using the recently developed structure theory for noiseless subsystems, the identification of such unitarily correctable subsystems is reduced to an algebraic exercise.

  • Received 4 August 2006

DOI:https://doi.org/10.1103/PhysRevA.74.042329

©2006 American Physical Society

Authors & Affiliations

David W. Kribs1,2 and Robert W. Spekkens3

  • 1Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1
  • 2Institute for Quantum Computing, University of Waterloo, Ontario, Canada, N2L 3G1
  • 3Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge CB3 0WA, United Kingdom

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Issue

Vol. 74, Iss. 4 — October 2006

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