Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels
Abstract
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely positive linear map, where the dimension of the underlying Hilbert space is a prime number. On such a quantum channel, the highest fidelity of a quantum error-correcting code of length and rate R is proven to be lower bounded by 1 - \exp [-n E(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. The result of this work applies to general discrete memoryless channels, including channel models derived from a physical law of time evolution, or from master equations.
Cite
@article{arxiv.quant-ph/0112103,
title = {Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels},
author = {Mitsuru Hamada},
journal= {arXiv preprint arXiv:quant-ph/0112103},
year = {2016}
}
Comments
19 pages, 2 figures. Ver.2: Comparisons with the previously known bounds and examples were added. Except for very noisy channels, this work's bound is, in general, better than those previously known. Ver.3: Introduction shortened. Minor changes