Entropy of Coherent States of Optical Fields

We consider statistical mixtures of two and three arbitrary coherent states that are the states of a data carrier in an optical communication channel. The eigenvalues and eigenvectors of the corresponding density operators are obtained in analytic form. For this purpose, an original parameterization of triangles on the complex phase plane is introduced. Analytic expressions are obtained for the von Neumann entropy of mixtures of two and three arbitrary coherent states, and its maximal value for a given average number of photons is calculated. It is found that the use of three coherent states for a given average number of photons ensures a larger capacity of an optical communication channel as compared to two states.