Probing the structure of entanglement with entanglement moments

TL;DR

This paper introduces entanglement moments, a new set of functions that quantify not just the presence but also the structure of entanglement in bipartite quantum states, with applications to measurement types and the Rabi model.

Contribution

It defines entanglement moments that provide detailed insights into how systems are entangled, extending traditional measures to include the nature and structure of entanglement.

Findings

Entanglement moments distinguish between projective and non-projective measurements.

They can be applied to analyze eigenstates of the Rabi model.

The moments are adaptable to any N-dimensional Hilbert space.

Abstract

We introduce and define a set of functions on pure bipartite states called entanglement moments. Usual entanglement measures tell you if two systems are entangled, while entanglement moments tell you both if and how two systems are entangled. They are defined with respect to a measurement basis in one system (e.g., a measuring device), and output numbers describing how a system (e.g., a qubit) is entangled with that measurement basis. The moments utilize different distance measures on the Hilbert space of the measured system, and can be generalized to any N-dimensional Hilbert space. As an application, they can distinguish between projective and non-projective measurements. As a particular example, we take the Rabi model's eigenstates and calculate the entanglement moments as well as the full distribution of entanglement.