Property of Classical Reliability Function for BPSK Signals Coded by Simplex Codes with SRM

There is a gap between properties of quantum and classical reliability functions. That is, the upper bound of the quantum reliability function diverges, whereas that of classical one does not, even if the same coherent signal is used. We are interested in the origin of this gap. In this paper, we investigate the upper bound of the reliability function for quantum signals coded by simplex codes when using square-root measurement (SRM). The reliability function in this case has a much steeper slope with respect to the rate than in the uncoded case. This result suggests the divergence of the upper bound of the quantum reliability function in the previous study.