Hierarchies of Geometric Entanglement
M. Blasone, F. Dell'Anno, S. De Siena, F. Illuminati

TL;DR
This paper introduces a hierarchical set of geometric measures to quantify and distinguish different types of entanglement in multipartite quantum states, providing new insights into the structure and ordering of entanglement in various quantum states.
Contribution
It develops a comprehensive framework of generalized geometric entanglement measures that hierarchically quantify bipartite and multipartite entanglement in pure quantum states.
Findings
Establishes a hierarchy between GHZ and W states based on geometric entanglement.
Provides a method for explicit evaluation of multipartite geometric entanglement components.
Shows scale invariance and self-similarity of entanglement in symmetric states.
Abstract
We introduce a class of generalized geometric measures of entanglement. For pure quantum states of elementary subsystems, they are defined as the distances from the sets of -separable states (). The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows to discriminate among the different contributions. The extended measures are applied to the study of entanglement in different classes of -qubit pure states. These classes include and states, and their symmetric superpositions; symmetric multi-magnon states; cluster states; and, finally, asymmetric generalized -like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement,…
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