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Lower bounds on the quantum capacity and highest error exponent of general memoryless channels

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1 Author(s)
Hamada, M. ; Quantum Comput. & Inf. Project, Japan Sci. & Technol. Corp., Tokyo, Japan

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 (CP) 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[-nE(R)+o(n)] for some function E(R). The E(R) is positive below some threshold R0, a direct consequence of which is that R0 is a lower bound on the quantum capacity. This is an extension of the author's earlier result. While the earlier work states the result for the depolarizing channel and a slight generalization of it (Pauli channels), the result of this work applies to general discrete memoryless channels, including channel models derived from a physical law of time evolution.

Published in:

Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 9 )

Date of Publication:

Sep 2002

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