Fermionic Entanglement and Correlation

TL;DR

This paper explores how entanglement is defined among indistinguishable fermions, introducing particle and mode pictures, and applies these concepts to molecular systems and electronic structure analysis.

Contribution

It clarifies two natural frameworks for fermionic entanglement and demonstrates their utility in resolving molecular correlation issues and analyzing electronic structures.

Findings

Fermionic entanglement can be characterized via particle and mode pictures.

Both pictures provide insights into electron correlation in atoms and molecules.

Application to molecular dissociation resolves the correlation paradox.

Abstract

Entanglement plays a central role in numerous fields of quantum science. However, as one departs from the typical "Alice versus Bob" setting into the world of indistinguishable fermions, it is not immediately clear how the concept of entanglement is defined among these identical particles. Our endeavor to recover the notion of subsystems, or mathematically speaking, the tensor product structure of the Hilbert space, lead to two natural pictures of defining fermionic entanglement: the particle picture and the mode picture. In the particle picture, entanglement characterizes the deviation of a fermionic quantum state from the non-interacting ones, e.g., single Slater determinants. In the mode picture, we recover the notion of subsystems, by referring to the partitioning of the orbital/mode that the fermions occupy, which allows us to naturally adopt the formalism of entanglement between distinguishable constituents. Both pictures reveal essential and interconnected aspects of fermionic entanglement, and thus offer precise tools for studying electron entanglement in highly relevant systems such as atoms and molecules. We showcase here two applications: i) resolving the correlation paradox in the molecular dissociation limit, ii) quantitative electronic structure analysis with orbital entanglement.