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Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels

Mitsuru Hamada
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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 $n$ 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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Mitsuru Hamada. 2002-06-21. Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels. https://doi.org/10.1109/tit.2002.801470

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