Transformation formulae for quantum noise representation in phase space

The phase space representation of quantum states is one of the most useful methods to describe the quantum noise properties in the quantum communication theory, and it enables an understanding of their properties with the classical analogy. In principle, however, this method can treat only quantum noise of quadrature components. Caves has discussed a method of transformation from quantum noises of quadrature amplitudes to those of photon and phase. The authors clarify the applicability of Caves´ formulae for some significant quantum states for a quantum communication viewpoint