  We consider information characteristics of single qudit state (spin j=9/2),
such as von Neumann entropy, von Neumann mutual information. We review
different mathematical properties of these information characteristics:
subadditivity and strong subadditivity conditions, Araki-Lieb inequality. The
inequalities are entropic inequalities for composite systems (bipartite,
tripartite), but they can be written for noncomposite systems. Using the
density matrix, describing the noncomposite qudit system state in explicit
matrix form we proved new entropic inequalities for single qudit state (spin
j=9/2). In addition, we also consider the von Neumann information of a qudit
toy model as a function of a real parameter. The obtained inequalities describe
the quantum hidden correlations in the single qudit system.
