Entangled graphs: Bipartite entanglement in multi-qubit systems
| Authors | |
|---|---|
| Year of publication | 2003 |
| Type | Article in Periodical |
| Magazine / Source | Physocal Review A |
| MU Faculty or unit | |
| Citation | |
| Field | Informatics |
| Keywords | quantum entanglement; mupli-partite systems |
| Description | 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 {\em 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 {\em linearly} with the number of entangled pairs. |
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