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.

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

References in corpus (6)

• The structure of multidimensional entanglement in multipartite systems
• Four-qubit entanglement from string theory
• Tensor Rank and Stochastic Entanglement Catalysis for Multipartite Pure States
• Tripartite entanglement transformations and tensor rank
• Geometric descriptions of entangled states by auxiliaries varieties
• Entanglement of three-qubit geometry

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