Entangled graphs: Bipartite entanglement in multi-qubit systems

Details Entangled graphs: Bipartite entanglement in multi-qubit systems Entangled graphs: Bipartite entanglement in multi-qubit systems

2002-11-05

arxiv.org/abs/quant-ph/0211020v1

Phys. Rev. A 67, 012322-1--6 (2003).

Physics

Quantum Physics

6 revtex pages, 2 figures, to appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.67.012322

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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