Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry
2 NOV 2020
14:00 - 15:00
In this talk, we present a novel entanglement classification of ?generic? n-qubit pure states under stochastic local operation and classical communication (SLOCC) that is based on a finite number of families and subfamilies, i.e., a fine-structure classification. To this end, we employ algebraic-geometry tools that are SLOCC invariants. Particularly, the families and subfamilies will be identified by k-secant varieties and ℓ-multilinear ranks, respectively. Not only does this method facilitate the classification of multipartite entanglement, but it also turns out to be operationally meaningful as it quantifies entanglement as a resource.