Classification of multipartite systems featuring only $|W⟩$ and $|GHZ⟩$ genuine entangled states

Abstract

In this paper we present several multipartite quantum systems featuring the same type of genuine (tripartite) entanglement. Based on a geometric interpretation of the so-called $|W⟩$ and $|GHZ⟩$ states we show that the classification of all multipartite systems featuring those and only those two classes of genuine entanglement can be deduced from earlier work of algebraic geometers. This classification corresponds in fact to classification of fundamental subadjoint varieties and establish a connection between those systems, well known in Quantum Information Theory and fundamental simple Lie algebras.

21 pages, 1 figure, 6 Tables

References in corpus (15)

• General criterion for the entanglement of two indistinguishable particles
• Quantifying entanglement resources
• Constructing N-qubit entanglement monotones from anti-linear operators
• Four-qubit entanglement from string theory
• Black Holes, Qubits and Octonions
• Strings, Black Holes, and Quantum Information
• On polynomial invariants of several qubits
• E_7 and the tripartite entanglement of seven qubits
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Three fermions with six single particle states can be entangled in two inequivalent ways
• E_6 and the bipartite entanglement of three qutrits
• A three-qubit interpretation of BPS and non-BPS STU black holes
• Geometric descriptions of entangled states by auxiliaries varieties
• Entanglement classification of three fermions with up to nine single-particle states
• Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case

Cited by in corpus (2)

• Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)
• Zoology of Atlas-groups: dessins d'enfants, finite geometries and quantum commutation