Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes
Abstract
On a class of memoryless quantum channels which includes the depolarizing channel, the highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function E(R). The E(R) is positive below some threshold R', which implies R' is a lower bound on the quantum capacity.
Cite
@article{arxiv.quant-ph/0109114,
title = {Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes},
author = {Mitsuru Hamada},
journal= {arXiv preprint arXiv:quant-ph/0109114},
year = {2009}
}
Comments
Ver.4. In vers.1--3, I claimed Theorem 1 for general quantum channels. Now I claim this only for a slight generalization of depolarizing channel in this paper because Lemma 2 in vers.1--3 was wrong; the original general statement is proved in quant-ph/0112103. Ver.5. Text sectionalized. Appeared in PRA. The PRA article is typographically slightly crude: The LaTeX symbol star, used as superscripts, was capriciously replaced by the asterisk in several places after my proof reading