The Necessary and Sufficient Conditions of Separability for Multipartite Pure States

Abstract

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.

Submitted to PRL in Sep. 2004, the paper No is LV9637. Submitted to SIAM on computing, in Jan., 2005, the paper No. is SICOMP 44687. Under reviewing now

References in corpus (2)

• Inductive Entanglement Classification of Four Qubits under SLOCC
• Inductive classification of multipartite entanglement under SLOCC

Cited by in corpus (4)

• SLOCC invariant and semi-invariants for SLOCC classification of four-qubits
• The Simple Criteria of SLOCC Equivalence Classes
• Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
• Polynomial method to study the entanglement of pure N-qubit states