Quantum Channel Capacity of Very Noisy Channels
arXiv:quant-ph/9706061 · doi:10.1103/PhysRevA.57.830
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.
31 pages including epsf postscript figures. Replaced to correct important typographical errors in equations 36, 37 and in text
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