Entanglement of Spatial Regions vs. Entanglement of Particles

TL;DR

This paper demonstrates that the leading order Rényi entropies of spatial regions containing a single particle match quantum mechanical predictions, suggesting a new way to measure entanglement of indistinguishable particles via spatial region entropy.

Contribution

It shows that spatial region entropies in quantum field theory reflect particle entanglement, bridging quantum field and quantum mechanical descriptions.

Findings

Leading order Rényi entropies match quantum mechanical results after vacuum subtraction.

Subleading corrections depend on wave function overlap.

Spatial region entropy can measure entanglement of indistinguishable particles.

Abstract

Consider an arbitrary local quantum field theory with a gap or an arbitrary gapless free theory. We consider states in such a theory, that describe two entangled particles localized in disjoint regions of space. We show that in such a state, to leading order, R\'{e}nyi entropies of spatial regions, containing only one of the particles are same as their quantum mechanical counterparts, after subtraction of vacuum contribution. Subleading corrections depend on overlap of wave functions. These results suggest that Von Neumann entropy of a spatial region, after subtraction of vacuum contribution, can serve as a measure of entanglement of indistinguishable particles in pure states.