The geometric measure of multipartite entanglement and the singular values of a hypermatrix

Abstract

It is shown that the geometric measure of entanglement of a pure multipartite state satisfies a polynomial equation, generalising the characteristic equation of the matrix of coefficients of a bipartite state. The equation is solved for a class of three-qubit states.

18 pages. Significant correction made; our results now agree with those of Tamaryan et al

References in corpus (7)

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• Estimating entanglement measures in experiments
• Universal geometric entanglement close to quantum phase transitions
• The geometric measure of entanglement for a symmetric pure state with positive amplitudes
• Maximally entangled three-qubit states via geometric measure of entanglement
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Cited by in corpus (8)

• Geometric measure of entanglement for pure multipartite states
• Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States
• Classification of Entanglement in Symmetric States
• How entangled can a multi-party system possibly be?
• Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
• Calculating Entanglement Eigenvalues for Non-Symmetric Quantum Pure States Based on the Jacobian Semidefinite Programming Relaxation Method
• Completely mixed state is a critical point for three-qubit entanglement