The distance between two signals on the quantum and the classical communication theory

In order to build a new standard of evaluation for the distinction of signals, the authors propose the orthogonality on quasi-phase space, which corresponds to the inner product on the Hilbert space. Hence the quasi-phase space is the generalized signal space where some concepts of quantum theory work. This orthogonality has great advantages of making possible to define the distance between two signals without a precise representation of the quantum state and providing a very convenient method of analysis of quantum communication systems. Moreover, since the mathematical structure of the orthogonality is similar to that of the Bhattacharyya distance in the classical theory, the authors discuss whether it is possible or not to apply the orthogonality to the conventional communication system