How are Entanglement Entropies Related to Entropy Bounds?

TL;DR

This paper explores how entanglement entropies relate to the covariant entropy bound, debating whether the bound is epistemic or ontological, and examining implications from area laws and spacetime emergence.

Contribution

It analyzes different interpretations of the entropy bound through entanglement entropy, connecting area laws and spacetime emergence to epistemic and ontological perspectives.

Findings

Area laws suggest an epistemic interpretation of the bound.

Entanglement may influence spacetime metric, supporting an ontological view.

Entanglement alone might not determine spacetime topology.

Abstract

In this paper we seek to understand what current knowledge of entanglement entropies suggests about the appropriate way to interpret the covariant entropy bound. We first begin by arguing that just as in the classical case, a universal bound on the von Neumann entropy could have either an epistemic or ontological origin. We then consider several possible ways of explaining the bound as a consequence of features of the entanglement entropy. We discuss consider area laws in condensed matter and quantum field theory, arguing that they suggest an epistemic reading of the bound. We also discuss the 'spacetime from entanglement' programme, arguing that entanglement alone may not be able to full ground spacetime topology, but it could potentially play a role in determining the spacetime metric, in which case it would potentially support a more ontological reading of the bound.