An Algebraic-Geometric Characterization of Tripartite Entanglement

Abstract

To characterize entanglement of tripartite ${\mathbb{C}}^d\otimes {\mathbb{C}}^d\otimes {\mathbb{C}}^d$ systems, we employ algebraic-geometric tools that are invariants under Stochastic Local Operation and Classical Communication (SLOCC), namely $k$-secant varieties and one-multilinear ranks. Indeed, by means of them, we present a classification of tripartite pure states in terms of a finite number of families and subfamilies. At the core of it stands out a fine-structure grouping of three-qutrit entanglement.

arXiv commentIt's a companion to arXiv:1910.09665 - Published version (10 pages, 2 figures, 2 tables)

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