Trade-off between the tolerance of located and unlocated errors in nondegenerate quantum error-correcting codes

Haselgrove, Henry L. and Rohde, Peter P. (2008) Trade-off between the tolerance of located and unlocated errors in nondegenerate quantum error-correcting codes. Quantum Information & Computation, 8 5: 0399-0410.


Author Haselgrove, Henry L.
Rohde, Peter P.
Title Trade-off between the tolerance of located and unlocated errors in nondegenerate quantum error-correcting codes
Journal name Quantum Information & Computation
ISSN 1533-7146
Publication date 2008-05-01
Sub-type Article (original research)
Open Access Status Not yet assessed
Volume 8
Issue 5
Start page 0399
End page 0410
Total pages 12
Editor R. Cleve
S. Braunstein
I. Cirac
Place of publication Paramus, N. J., USA
Publisher Rinton Press
Language eng
Subject C1
020603 Quantum Information, Computation and Communication
970102 Expanding Knowledge in the Physical Sciences
Abstract In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of depolarization noise. This raises the question of which general properties of quantum error-correcting codes might explain such an apparent trade-off between tolerance to located and unlocated error types. We extend the counting argument behind the well-known quantum Hamming bound to derive a bound on the weights of combinations of located and unlocated errors which are correctable by nondegenerate quantum codes. Numerical results show that the bound gives an excellent prediction to which combinations of unlocated and located errors can be corrected {\em with high probability} by certain large degenerate codes. The numerical results are explained partly by showing that the generalized bound, like the original, is closely connected to the information-theoretic quantity the {\em quantum coherent information}. However, we also show that as a measure of the exact performance of quantum codes, our generalized Hamming bound is provably far from tight.
Keyword Quantum information
Quantum computing
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: 2009 Higher Education Research Data Collection
Centre for Quantum Computer Technology Publications
 
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Created: Sat, 21 Mar 2009, 01:58:39 EST by Ruth Forrest on behalf of ARC Ctr of Excell for Quantum Computer Technology