  We compare the entropy-energy inequality and the von Neumann entropic
inequality for three level atom implemented on superconducting circuits with
Josephson junction. The positivity of entropy and energy relations for the
qutrit system are used for verification of state tomography of qudit systems.
The results obtained are valid for generic quantum states (qudits) and are
illustrated on the example of the temperature density matrix of the single
qutrit state.
