Geometric Measure of Entanglement and Shared Quantum States

Abstract

We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different expressions depending on the range of definition in parameter space. Each expression of the measure has its own geometrically meaningful interpretation. Such an interpretation allows oneself to take one step toward a complete understanding for the general properties of the entanglement measure. The states that lie on joint surfaces separating different ranges of definition, designated as shared states, seem to have particularly interesting features. The properties of the shared states are fully discussed.

13 pages, 2 figure, will appear in PRA, many references added, new results are included, style is improved

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Cited by in corpus (12)

• Maximally entangled three-qubit states via geometric measure of entanglement
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
• The geometric measure of multipartite entanglement and the singular values of a hypermatrix
• Duality and the geometric measure of entanglement of general multiqubit W states
• Mixed-State Entanglement and Quantum Teleportation through Noisy Channels
• Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition
• Generalized Schmidt decomposition based on injective tensor norm
• Toward an understanding of entanglement for generalized n-qubit W-states
• Perfect Quantum Teleportation and Superdense coding with $P_{max}=1/2$ states
• Completely mixed state is a critical point for three-qubit entanglement
• Effect of Phase Factor in the Geometric Entanglement Measure of Three-Qubit States
• Role of Three-Qubit Mixed-States Entanglement in Teleportation Scheme