Simplification of the Calculation of the Channel Matrix for AMPM Coherent-state Signals

The square-root measurement (SRM) is regarded as the optimum quantum measurement for symmetric signals and quasi-optimum measurements for any quantum signals. Therefore, deriving formulae for the channel matrix by using SRM is crucial in developing a theory of quantum communications. To date, formulae for these matrices are known for symmetric and group-covariant signals. However, there are important non-symmetric signals such as ASK, AMPM, and QAM signals, etc. In this paper, we demonstrate that the calculation of the channel matrix for 4m-ary AMPM signals can be simplified by using their partial symmetry.