  The two-parameter Minkowski like inequality written for composite quantum
system state is obtained for arbitrary Hermitian nonnegative matrix with trace
equal to unity. The inequality can be used as entropic and information
inequality for density matrix of noncomposite finite quantum system, e.g., for
a single qudit state. The analogs of strong subadditivity condition for the
single qudit is discussed in context of obtained Minkowski like inequality.
