The Necessary and Sufficient Conditions of Separability for Multipartite Pure States

Physics – Quantum Physics

Scientific paper

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Submitted to PRL in Sep. 2004, the paper No is LV9637. Submitted to SIAM on computing, in Jan., 2005, the paper No. is SICOMP

Scientific paper

In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a necessary condition for a local unitary equivalence class for a bipartite system in terms of the determinant of the matrix of amplitudes and explore a variance as a measure of entanglement for multipartite pure states.

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