Applying a symmetrization method by coding to non-symmetric mixed-state signals

In quantum communication theory, group covariant signals are important and useful when we consider the minimization problem of the error probability or the maximization problem of the mutual information. However, in practical applications, there are important non-symmetric signals such as amplitude shift keying or quadrature amplitude modulation signals. To manage this situation, we have proposed a symmetrization method of non-symmetric pure-state signals by using coding. In this paper, we consider to apply the symmetrization method to mixed-state signals and give a necessary condition of mixed-state signals to apply the method. Then, we present examples of mixed-state signals to which the symmetrization method can be applied.