Probability Representation of Quantum Mechanics and the Quantizer-Dequantizer Formalism

A review of the approach where the states of quantum systems are identified with fair probability distributions is presented. The quantizer-dequantizer operators used to construct the invertible map of the density operators onto the probability distributions are applied to obtain the kinetic equations for probability distributions identified with the quantum system states. For qubit states, the von Neumann evolution equation for the density operator is explicitly given in the form of kinetic equation for the probability distribution. Simplest tomographic probability distributions describing the states of multimode quantum oscillator are constructed.