Towards a Proof of the Improved Quantum Null Energy Condition

TL;DR

This paper discusses the proof of the Improved Quantum Null Energy Condition (INEC), a stronger energy condition in quantum field theory, based on properties of relative entropy and modular Hamiltonians, and explores its implications for quantum focusing.

Contribution

The paper provides a proof of the INEC under an additional assumption and explores its relation to the quantum focusing conjecture.

Findings

INEC holds under an extra assumption relating EMT to relative entropy.

The paper links INEC with the quantum focusing conjecture.

Speculates on a modified Quantum Focusing Conjecture based on INEC and QNEC.

Abstract

The Improved Quantum Null Energy Condition (INEC) was recently derived from the (restricted) quantum focusing conjecture (QFC), and is a statement about the energy-momentum tensor (EMT) of field theories in Minkowski space-time. It is a stronger condition than the quantum null energy condition (QNEC), and includes the possibility of expanding or contracting geodesics. Using the properties of relative entropy and modular Hamiltonian associated with null deformation of the sphere, we show the INEC holds under an additional assumption relating the EMT to the relative entropy. Furthermore, using the QNEC and INEC as a basis, we briefly speculate about a possible modified Quantum Focusing Conjecture.