Structural Quantification of Entanglement

TL;DR

This paper presents a new method for detailed structural and quantitative analysis of multipartite entanglement, enabling the distinction and measurement of different entanglement structures in complex quantum states.

Contribution

The authors develop a framework for constructing optimal witnesses to identify and quantify various entanglement structures, including in noisy and multimode continuous variable systems.

Findings

Derived equations for optimal entanglement witnesses.

Successfully analyzed entanglement in 4-cluster states with noise.

Demonstrated applicability to multimode continuous variable states.

Abstract

We introduce an approach which allows a detailed structural and quantitative analysis of multipartite entanglement. The sets of states with different structures are convex and nested. Hence, they can be distinguished from each other using appropriate measurable witnesses. We derive equations for the construction of optimal witnesses and discuss general properties arising from our approach. As an example, we formulate witnesses for a 4-cluster state and perform a full quantitative analysis of the entanglement structure in the presence of noise and losses. The strength of the method in multimode continuous variable systems is also demonstrated by considering a dephased GHZ-type state.