Information and two-level systems

I consider the general functions depending on the quantum state represented by a two-level density matrix. Quantities of relevance are state distance and informations measures, i.e. entropies. I introduce a new complex representation of such functions. Utilizing the geometric interpretation of complex mappings, I summarize several properties of such transformations of the state. In particular these results are used to suggest several possible applications to physical questions. These are tentative only, but they indicate the physical relevance of the mathematical results presented.