R\'enyi generalizations of quantum information measures

TL;DR

This paper develops Re9nyi generalizations of quantum information measures, extending their applicability in physics, and explores their properties and potential applications, including conjectures about their monotonicity.

Contribution

It introduces a systematic way to generalize quantum information measures using Re9nyi entropies and analyzes their properties and potential uses.

Findings

Proposed Re9nyi generalizations for measures with linear entropy combinations.

Analyzed properties of Re9nyi conditional quantum mutual information.

Conjectured and proved monotonicity in the Re9nyi parameter for special cases.

Abstract

Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in applications. We prescribe R\'enyi generalizations for any quantum information measure which consists of a linear combination of von Neumann entropies with coefficients chosen from the set {-1,0,1}. As examples, we describe R\'enyi generalizations of the conditional quantum mutual information, some quantum multipartite information measures, and the topological entanglement entropy. Among these, we discuss the various properties of the R\'enyi conditional quantum mutual information and sketch some potential applications. We conjecture that the proposed R\'enyi conditional quantum mutual informations are monotone increasing in the R\'enyi parameter, and we have proofs of this conjecture for some special cases.