  We begin with the simple model of phase sychronization in open classical
nonlinear system which is represented in the language of angular momentum
variables. After that we propose the relevant quantum counterpart of this
system. Using the appropriate Lindblad master equation for the density matrix
of two qubit realization of such system we have revealed that stationary state
of this composite system is pure and entangled with small dispersion of phase
observable. We believe that such curious connection between entangled
stationary states of quantum composite system and phase sychronization between
its subsystems may be typical for rather wide class of similar nonlinear open
systems as well.
