On the general form of the dynamical transformation of density matrices

A study is made of the most general linear transformations of the density matrices of a quantum system that preserve the total probability and do not generate negative probabilities. The general form of such transformations is found in the case of a two-dimensional state space. It is shown that if the state space has more than six dimensions, this form loses its generality. Individual properties of dynamical transformations in the infinite–dimensional case are described.