  The notion of weighted quantum entropy is reviewed and considered for
bipartite and noncomposite quantum systems. The known for the weighted entropy
information inequality (subadditivity condition) is extended to the case of
indivisible qudit system on example of qutrit. This new inequality for qutrit
density matrix is discussed for different cases of weights and states. The role
of weighted entropy is discussed in connection with studies of nonlinear
quantum channels.
