On Testing Entropic Inequalities for Superconducting Qudit

TL;DR

This paper experimentally tests new entropic inequalities for superconducting qudits, extending their application from bipartite systems to non-composite systems, and explores their use in assessing data accuracy and correlations.

Contribution

It provides the first experimental verification of entropic inequalities in superconducting qudits, demonstrating their applicability beyond bipartite systems.

Findings

Confirmed the validity of entropic inequalities for superconducting qudits

Showed that mutual information can characterize correlations in noncomposite systems

Validated the use of these inequalities for data accuracy assessment

Abstract

The aim of this work is to verify the new entropic and information inequalities for non-composite systems using experimental $5 \times 5$ density matrix of the qudit state, measured by the tomographic method in a multi-level 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, may charachterize correlations between different degrees of freedom in a noncomposite system.