Quantum Channel Capacity of Very Noisy Channels
Abstract
We present a family of additive quantum error-correcting codes whose capacities exceeds that of quantum random coding (hashing) for very noisy channels. These codes provide non-zero capacity in a depolarizing channel for fidelity parameters when . Random coding has non-zero capacity only for ; 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 non-random (cat) code within a random code to obtain good codes. The cat code with block size five is shown to be optimal for 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.
Cite
@article{arxiv.quant-ph/9706061,
title = {Quantum Channel Capacity of Very Noisy Channels},
author = {David P. DiVincenzo and Peter W. Shor and John A. Smolin},
journal= {arXiv preprint arXiv:quant-ph/9706061},
year = {2009}
}
Comments
31 pages including epsf postscript figures. Replaced to correct important typographical errors in equations 36, 37 and in text