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