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arXiv · 2106.14891

An Algebraic-Geometric Characterization of Tripartite Entanglement

Masoud Gharahi·Stefano Mancini
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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 $k$-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.

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Masoud Gharahi, Stefano Mancini. 2021-06-28. An Algebraic-Geometric Characterization of Tripartite Entanglement. https://doi.org/10.1103/physreva.104.042402

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