Deformed entropy and information relations for composite and noncomposite systems

TL;DR

This paper extends the concept of conditional entropy to noncomposite quantum systems, deriving new entropic inequalities and relations, including for single qudit states and systems without subsystems, broadening the understanding of quantum information measures.

Contribution

It introduces a generalized framework for entropy and information relations applicable to noncomposite and single qudit systems, expanding quantum information theory.

Findings

Derived q-deformed entropic inequalities for noncomposite systems

Established entropic inequalities for quantum tomograms of qudit states

Formulated the Araki–Lieb inequality for systems without subsystems

Abstract

The notion of conditional entropy is extended to noncomposite systems. The q-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the noncomposite systems. New entropic inequalities for quantum tomograms of qudit states including the single qudit states are obtained. The Araki{Lieb inequality is found for systems without subsystems.