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Information-theoretic interpretation of quantum error-correcting codes

Cerf, Nicolas J. and Cleve, Richard (1997) Information-theoretic interpretation of quantum error-correcting codes. Physical Review A, 56 (3). pp. 1721-1732. ISSN 1050-2947. doi:10.1103/PhysRevA.56.1721.

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Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while clarifying the differences between classical and quantum codes. More specifically, it is shown how quantum information theory accounts for the fact that “redundant” information can be distributed over quantum bits even though this does not violate the quantum “no-cloning” theorem. Such a remarkable feature, which has no counterpart for classical codes, is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state. This information-theoretic description of quantum coding is used to derive the quantum analog of the Singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors.

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Additional Information:©1997 The American Physical Society Received 14 February 1997 We acknowledge C. Adami and J. Preskill for very useful discussions. We thank the organizers of the ITP program on Quantum Computers and Decoherence for their invitation in Santa Barbara, where this work has been performed. This research was supported in part by the National Science Foundation under Grant Nos. PHY 94-12818, PHY 94-20470 and PHY 94-07194, and by a grant from DARPA/ARO through the QUIC Program (No. DAAH04-96-1-3086).
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Deposited On:20 Oct 2006
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