Monotonicity of the von Neumann entropy expressed as a function of R\'enyi entropies

TL;DR

This paper investigates how the von Neumann entropy relates monotonically to Re9nyi entropies of different orders, revealing a pattern of increasing or decreasing behavior based on the parity of the order.

Contribution

It establishes the monotonicity properties of von Neumann entropy as a function of Re9nyi entropies of various orders, providing new insights into their relationship.

Findings

Von Neumann entropy increases with even-order Re9nyi entropies.

Von Neumann entropy decreases with odd-order Re9nyi entropies.

The relationship depends on the parity of the Re9nyi entropy order.

Abstract

The von Neumann entropy of a density matrix of dimension d, expressed in terms of the first d-1 integer order R\'enyi entropies, is monotonically increasing in R\'enyi entropies of even order and decreasing in those of odd order.