  The aim of this work is to verify the new entropic and information
inequalities for non-composite systems using experimental $5 \times 5$ density
matrix of the qudit state, measured by the tomographic method in a multi-level
superconducting circuit. These inequalities are well-known for bipartite and
tripartite systems, but have never been tested for superconducting qudits.
Entropic inequalities can also be used to evaluate the accuracy of experimental
data and the value of mutual information, deduced from them, may charachterize
correlations between different degrees of freedom in a noncomposite system.
