Inequalities for nonnegative numbers and information properties

TL;DR

This paper develops new inequalities for nonnegative numbers and applies them to quantum information, deriving novel entropic inequalities for qudit states that reveal quantum correlations and properties.

Contribution

It introduces new inequalities for nonnegative numbers and applies them to quantum tomograms, leading to novel entropic inequalities for qudit states and quantum correlations.

Findings

Derived new inequalities for quantum tomograms.

Established bounds for Shannon, Renyi, and Tsallis entropies.

Characterized quantum correlations beyond known measures.

Abstract

We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The inequalities characterize the degree of quantum correlations in addition to noncontextuality and quantum discord. We use the subadditivity and strong subadditivity conditions for qudit tomographic-probability distributions depending on the unitary-group parameters in order to derive new inequalities for Shannon, Renyi, and Tsallis entropies of spin states.