Qutrits in multiparticle systems

The evolution of complex composite quantum systems which can be reduced to systems with a small dimensionality of the Hilbert space (of the qutrit, ququart type, etc.) is considered. In the case of the interaction of an ensemble of two-level atoms with light, the conditions are found under which a qutrit is produced from the light and atomic states. The properties and possible applications of a qutrit based of the Fock states of light in which two photons are distributed among three modes are discussed. It is shown that this state has the nonclassical photon statistics, is entangled and can be used as a quantum channel for the teleportation, dense coding, and key distribution.