INFORMATION-THEORETIC INTERPRETATION OF QUANTUM ERROR-CORRECTING CODES

Quantum error-correcting codes are analyzed from an information-theore tic 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 informat ion theory accounts for the fact that ''redundant'' information can be distributed over quantum bits even though this does not violate the q uantum ''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 stat e. This information-theoretic description of quantum coding is used to derive the quantum analog of the Singleton bound on the number of log ical bits that can be preserved by a code of fixed length which can re cover a given number of errors.