title: Entanglement classification with matrix product states.
abstract: We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for N parties carry over to the N + 1 case. Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by .
authors.affiliation: Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Sanz
authors.affiliation: Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain.
authors.forename: I L
authors.initials: IL
authors.lastname: Egusquiza
authors.affiliation: Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain.
authors.forename: R
authors.initials: R
authors.lastname: Di Candia
authors.affiliation: Department of Optics, Faculty of Science, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic.|Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), University of Paderborn, Warburger Straβe 100, 33098 Paderborn, Germany.
authors.forename: H
authors.initials: H
authors.lastname: Saberi
authors.affiliation: Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain.
authors.forename: L
authors.initials: L
authors.lastname: Lamata
authors.affiliation: Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain.|IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain.
authors.forename: E
authors.initials: E
authors.lastname: Solano