Entropy-energy inequality for superconducting qutrit

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.