Testing Entropic Inequalities for Superconducting Qudits

We verify the new entropic and information inequalities for noncomposite systems using an experimental 5×5 density matrix of the qudit state measured by the tomographic method in a multilevel superconducting circuit. These inequalities are well known for bipartite and tripartite systems but have never been tested for superconducting qudits. Entropic inequalities can also be used to evaluate the accuracy of experimental data and the value of mutual information deduced from them and characterize correlations between different degrees of freedom in a noncomposite system.