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New quantum entropic inequality for states of system of n >_ 1 qudits isobtained. The inequality has the form of quantum subadditivity condition ofbipartite qudit system and coincides with this subadditivity condition for thesystem of two qudits. The general statement on existence of the subadditivitycondition for arbitrary probability distribution and arbitrary qudit-systemtomogram is formulated. The nonlinear quantum channels creating the entangledstates from separable ones are discussed.

Subadditivity condition for spin-tomograms and density matrices of arbitrary composite and noncomposite qudit systems