A Note on Entanglement Entropy, Coherent States and Gravity

TL;DR

This paper investigates the relationship between entanglement entropy, coherent states, and gravity, highlighting limitations of current derivations of Einstein's equations from entanglement principles and revealing additional contributions to entropy variations.

Contribution

It demonstrates that entanglement entropy of coherent states is stress-energy independent and explores the implications for deriving Einstein's equations from entanglement entropy principles.

Findings

Entanglement entropy of coherent states is independent of stress energy.

First order variations of Einstein's equations may not extend to finite variations in coherent states.

Additional contributions to entropy variation beyond previous models are identified.

Abstract

The entanglement entropy of a free quantum field in a coherent state is independent of its stress energy content. We use this result to highlight the fact that while the Einstein equations for first order variations about a locally maximally symmetric vacuum state of geometry and quantum fields seem to follow from Jacobson's principle of maximal vacuum entanglement entropy, their possible derivation from this principle for the physically relevant case of finite but small variations remains an open issue. We also apply this result to the context of Bianchi's identification, independent of unknown Planck scale physics, of the first order variation of Bekenstein Hawking area with that of vacuum entanglement entropy. We argue that under certain technical assumptions this identification seems not to be extendible to the context of finite but small variations to coherent states. Our particular method of estimation of entanglement entropy variation reveals the existence of certain contributions over and above those appearing in Jacobson's and Bianchi's works. We discuss the sense in which these contributions may be subleading to those already present in these works.