Physics – Quantum Physics
Scientific paper
2001-12-18
IEEE Trans. Information Theory, vol.48, no.9, pp.2547--2557, Sept. 2002
Physics
Quantum Physics
19 pages, 2 figures. Ver.2: Comparisons with the previously known bounds and examples were added. Except for very noisy channe
Scientific paper
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 $n$ 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.
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