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Entangled graphs: Bipartite entanglement in multi-qubit systems

Martin Plesch·Vladimir Buzek
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Abstract

Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite system is associated with a point (vertex) while a bi-partite entanglement between two specific qubits is represented by a connection (edge) between these points. We prove that any such entangled structure can be associated with a pure state of a multi-qubit system. Moreover, we show that a pure state corresponding to a given entangled structure is a superposition of vectors from a subspace of the $2^N$-dimensional Hilbert space, whose dimension grows linearly with the number of entangled pairs.

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Martin Plesch, Vladimir Buzek. 2002-11-05. Entangled graphs: Bipartite entanglement in multi-qubit systems. https://doi.org/10.1103/physreva.67.012322

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