How are Entanglement Entropies Related to Entropy Bounds?

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.