New inequality for density matrices of single qudit states
  Using the monotonity of relative entropy of composite quantum systems we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Example of qutrit state inequalities and the "qubit portrait" bound for the distance between the qutrit states are considered in explicit form. 
V. N. Chernega, O. V. Man'ko, V. I. Man'ko
quant-ph