Quantum-channel capacity of very noisy channels

被引:203
作者
DiVincenzo, DP [1 ]
Shor, PW
Smolin, JA
机构
[1] IBM Corp, Thomas J Watson Res Ctr, Yorktown Hts, NY 10598 USA
[2] AT&T Bell Labs, Res Ctr, Murray Hill, NJ 07974 USA
关键词
D O I
10.1103/PhysRevA.57.830
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We present a family of additive quantum error-correcting codes whose capacities exceed those of quantum random coding (hashing) for very noisy channels. These codes provide nonzero capacity in a depolarizing channel for fidelity parameters f when f>0.80944. Random coding has nonzero capacity only for f >0.81071; by analogy to the classical Shannon coding limit, this value had previously been conjectured to be a lower bound. We use the method introduced by Shor and Smolin of concatenating a nonrandom repetition (cat) code within a random code to obtain good codes. The cat code with block size five is shown to be optimal Cor single concatenation. The best known multiple-concatenated code we found has a block size of 25. We derive a general relation between the capacity attainable by these concatenation schemes and the coherent information of the inner code states.
引用
收藏
页码:830 / 839
页数:10
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