Entangled graphs: A classification of four-qubit entanglement

Abstract

We use the concept of \textit{entangled graphs} with weighted edges to present a classification for four-qubit entanglement which is based neither on the LOCC nor the SLOCC. Entangled graphs, first introduced by Plesch et al. [Phys. Rev. A 67, (2003) 012322], are structures such that each qubit of a multi-qubit system is represented as a vertex and an edge between two vertices denotes bipartite entanglement between the corresponding qubits. Our classification is based on the use of generalized Schmidt decomposition of pure states of multi-qubit systems. We show that for every possible entangled graph one can find a pure state such that the reduced entanglement of each pair, measured by concurrence, represents the weight of the corresponding edge in the graph. We also use the concept of tripartite and quadripartite concurrences as a proper measure of global entanglement of the states. In this case a circle including the graph indicates the presence of global entanglement.

11 pages, 2 figures, Minor changes from previous version

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Cited by in corpus (13)

• On the Black-Hole/Qubit Correspondence
• A Variational Approach to the Quantum Separability Problem
• Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry
• An Algebraic-Geometric Characterization of Tripartite Entanglement
• Classification of four qubit states and their stabilisers under SLOCC operations
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Entanglement Classification of Restricted Greenberger-Horne-Zeilinger Symmetric States in Four-Qubit System
• Classifying Entanglement by Algebraic Geometry
• Quantifying High-Order Interdependencies in Entangled Quantum States
• Modeling Tripartite Entanglement in Quantum Protocols using Evolving Entangled Hypergraphs
• The quantification of a genuine tetrapartite entanglement in a mixed spin-(1/2,1) Heisenberg tetramer
• Greenberger-Horne-Zeilinger Symmetry in Four Qubit System
• Monogamy constraints on entanglement of four-qubit pure states