PERFORMANCE OF CLASSICAL BINARY CODES FOR QUANTUM CHANNELS: TOWARD HIGHLY RELIABLE QUANTUM COMMUNICATIONS

摘要

Transmission of classical information via a quantum channel is one of the important issues in quantum information theory. Our particular interest lies in the classical coding - quantum decoding case. Fortunately, the channel coding theorem for this case has been already proven by Holevo and Schumacher-Westmoreland, and the reliability function has been formulated. Therefore our task is to find good codes predicted from this theorem for realizing highly reliable quantum communication systems. In this paper, the decoding error probabilities for several cases of Bose-Chaudhuri-Hocquenghem (BCH) codes and Reed-Muller (RM) codes are computed. Prom comparison with the bound on decoding error probability given by the reliability function, the codes examined in this paper are found to be good codes.