量子纠错码可达最高保真度的指数下界
量子物理
2009-11-07 v5
摘要
在一类包含去极化信道的无记忆量子信道上，证明了长度为 n、速率为 R 的量子纠错码的最高保真度下界为 1-exp[-nE(R)+o(n)]，其中 E(R) 为某函数。E(R) 在某阈值 R' 以下为正，这意味着 R' 是量子容量的一个下界。
引用
@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}
}
备注
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