Computable R\'enyi mutual information: Area laws and correlations

TL;DR

This paper introduces Renyi-based mutual information measures that satisfy area laws and bound correlations in quantum many-body systems, offering computational advantages over traditional von Neumann measures.

Contribution

It proposes Renyi divergence-based mutual information definitions that are computationally efficient and retain key properties, demonstrating their area law and correlation bounds.

Findings

Renyi mutual information obeys a thermal area law

It upper bounds all correlation functions

Efficient variational evaluation for matrix product states

Abstract

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on R\'enyi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.