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      An Algebraic-Geometric Characterization of Tripartite Entanglement

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          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 \(k\)-secants 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.

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          Author and article information

          Journal
          28 June 2021
          Article
          2106.14891
          75e8aac8-7aaa-406a-97eb-ad271aabe62e

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          10 pages, 2 figures, 2 tables
          quant-ph math-ph math.MP

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