Entangled graphs: A classification of four-qubit entanglement

Details Entangled graphs: A classification of four-qubit entanglement Entangled graphs: A classification of four-qubit entanglement

2010-03-14

arxiv.org/abs/1003.2762v1

Physics

Quantum Physics

10 pages, 2 figures

Scientific paper

In this paper we use the concept of \textit{entangled graphs} with weighted edges and present a classification of four-qubit entanglement. 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 (GSD) 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 fourpartite 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.

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