Connecting the von Neumann and Renyi entropies for Fermions

TL;DR

This paper investigates the relationship between von Neumann and Renyi entropies in Fermionic lattice systems, proposing methods to approximate the former using integer-order Renyi entropies and assessing the accuracy of these approximations.

Contribution

It introduces a novel approach to approximate von Neumann entropy through integer-order Renyi entropies in Fermionic systems and provides estimates for the approximation quality.

Findings

Established a relation between von Neumann and Renyi entropies for Fermions.

Provided bounds on the approximation error of von Neumann entropy using Renyi entropies.

Applied the method to shift-invariant quasi-free Fermionic lattice systems.

Abstract

We explore the relation between the von Neumann entropy and the Renyi entropies of integer orders for shift-invariant quasi-free Fermionic lattice systems. We investigate approximating the von Neumann entropy by a combination of integer-order Renyi entropies and give an estimate for the quality of such an approximation.