Weighted information and weighted entropic inequalities for qutrit and ququart states

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.