  We discuss some inequalities for N nonnegative numbers. We use these
inequalities to obtain known inequalities for probability distributions and new
entropic and information inequalities for quantum tomograms of qudit states.
The inequalities characterize the degree of quantum correlations in addition to
noncontextuality and quantum discord. We use the subadditivity and strong
subadditivity conditions for qudit tomographic-probability distributions
depending on the unitary-group parameters in order to derive new inequalities
for Shannon, Renyi, and Tsallis entropies of spin states.
