Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels
Abstract
Tradeoffs between the information rate and fidelity of quantum errorcorrecting 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 errorcorrecting code of length $n$ 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2001
 arXiv:
 arXiv:quantph/0112103
 Bibcode:
 2001quant.ph.12103H
 Keywords:

 Quantum Physics
 EPrint:
 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