Classification of quantum states based on the null energy condition

TL;DR

This paper investigates how quantum states influence the violation of the null energy condition in curved spacetimes, showing that coherent states do not violate it, while certain pure or mixed states can.

Contribution

It demonstrates that coherent quantum states do not violate the null energy condition, and identifies conditions under which pure or mixed states do violate it.

Findings

Coherent states do not violate the null energy condition.

Certain pure or mixed states can violate the null energy condition.

Discussion of dynamical violation of the null energy condition by quantum states.

Abstract

Violation of the null energy condition plays an important role both in the general theory of relativity and quantum field theory in curved spacetimes. Over the years, it has been shown that the violation of the null energy condition leads to instability and violation of causality. In quantum field theory, violation of the energy condition also depends on the quantum states apart from the geometry of curved spacetime. Hence, the quantum effects play an important role in the violation of the null energy condition. We show that the set of all the coherent states does not violate the null energy condition. Further, we also show that under certain conditions, the null energy condition is violated either by a pure state or a mixed state. Furthermore, the dynamical violation of the null energy condition by the quantum states is also discussed here.