Measuring entanglement along collective operators

TL;DR

This paper presents a novel framework for analyzing multiparty entanglement using collective variables and a graphical spectral space, enabling better detection and understanding of $k$-entanglement in various quantum systems.

Contribution

It introduces a spectral space approach for collective observable-based entanglement quantification, extending to mixed states and providing visual interpretation tools.

Findings

Effective assessment of $k$-entanglement through spectral properties.

Extension of entanglement inequalities to new scenarios.

Application to finite and infinite-dimensional quantum systems.

Abstract

We introduce a framework for the study of multiparty entanglement by analyzing the behavior of collective variables. Throughout the manuscript, we explore a specific type of multiparty entanglement which can be detected through the fluctuation of a collective observable. We thoroughly analyze its properties and how it can be extended to mixed states while placing it within the context of the existing literature. The novelty of our approach also lies in the fact that we present a graphical point of view. This is done by introducing a spectral space on which the various properties of our entanglement quantifier have a direct pictorial interpretation. Notably, this approach proves particularly effective for assessing $k$-entanglement, as we show its ability to extend previously established inequalities. To enhance understanding, we also demonstrate how this framework applies to specific scenarios, encompassing both finite-dimensional cases and infinite-dimensional systems, the latter being exemplified by the time-frequency modal degree of freedom of co-propagating single photons.