Information-theoretic interpretation of quantum error-correcting codes

Details Information-theoretic interpretation of quantum error-correcting codes Information-theoretic interpretation of quantum error-correcting codes

1997-02-13

arxiv.org/abs/quant-ph/9702031v2

Phys.Rev.A56:1721,1997

Physics

Quantum Physics

14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.56.1721

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 analogue 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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