Geometric measure of entanglement for pure multipartite states

Abstract

We provide methods for computing the geometric measure of entanglement for two families of pure states with both experimental and theoretical interests: symmetric multiqubit states with non-negative amplitudes in the Dicke basis and symmetric three-qubit states. In addition, we study the geometric measure of pure three-qubit states systematically in virtue of a canonical form of their two-qubit reduced states, and derive analytical formulae for a three-parameter family of three-qubit states. Based on this result, we further show that the W state is the maximally entangled three-qubit state with respect to the geometric measure.

A minor error on the explanation of three-qubit GHZ state has been corrected in the fourth paragraph of page 1. Thanks for Martin Aulbach pointing out this error

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Cited by in corpus (36)

• Multipartite entanglement measures
• A resource theory of entanglement with a unique multipartite maximally entangled state
• Entanglement in the symmetric sector of $n$ qubits
• Additivity and non-additivity of multipartite entanglement measures
• Multiqubit symmetric states with maximally mixed one-qubit reductions
• Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states
• Classification of Entanglement in Symmetric States
• A comparison of old and new definitions of the geometric measure of entanglement
• How entangled can a multi-party system possibly be?
• Decoherence dynamics of geometric measure of quantum discord and measurement-induced nonlocality for noninertial observers at finite temperature
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
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• Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states
• Theoretical and computational aspects of entanglement
• Proof of the Gour-Wallach conjecture
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• Geometric Entanglement of Symmetric States and the Majorana Representation
• Canonical form of three-fermion pure-states with six single particle states
• The Minimum Hartree Value for the Quantum Entanglement Problem
• An Extention of Entanglement Measures for Pure States
• Entanglement classes of symmetric Werner states
• Spin Squeezing by means of Driven Superradiance
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• All multipartite entanglements are quantum coherences in locally distinguishable bases
• The Quantum Eigenvalue Problem and Z-Eigenvalues of Tensors
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• Finding maximal quantum resources
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• Constructing $2\times 2\times 4$ and $4\times 4$ unextendible product bases and positive-partial-transpose entangled states
• Constructing unextendible product bases from multiqubit ones
• Linear response of tripartite entanglement to infinitesimal noise
• On orthogonal tensors and best rank-one approximation ratio