Fidelity of a t-error correcting quantum code with more than t errors
Quantum Physics
2009-11-06 v5
Abstract
It is important to study the behavior of a t-error correcting quantum code when the number of errors is greater than t, because it is likely that there are also small errors besides t large correctable errors. We give a lower bound for the fidelity of a t-error correcting stabilizer code over a general memoryless channel, allowing more than t errors. We also show that the fidelity can be made arbitrary close to 1 by increasing the code length.
Cite
@article{arxiv.quant-ph/0011047,
title = {Fidelity of a t-error correcting quantum code with more than t errors},
author = {Ryutaroh Matsumoto},
journal= {arXiv preprint arXiv:quant-ph/0011047},
year = {2009}
}
Comments
9 pages, ReVTeX4 beta 5. To be published in Phys. Rev. A. The lower bound is made tighter in version 4 and 5. All approximations in the first version are removed, and a lower bound for the average of the fidelity is given in the second version. A critical error is corrected