Observable measures of multipartite entanglement

TL;DR

This paper develops observable, experimentally accessible bounds for quantifying multipartite entanglement in quantum systems of arbitrary size, using state purities and correlation functions.

Contribution

It introduces new bounds based on local and global purities, entropy inequalities, and monogamy relations to quantify various degrees of multipartite entanglement.

Findings

Bounds successfully applied to GHZ, Dicke, W states, and random states.

Bounds provide practical tools for entanglement quantification without full state tomography.

Numerical and analytical tests confirm the effectiveness of the bounds.

Abstract

Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.