Geometric Measure of Entanglement and Shared Quantum States

Details Geometric Measure of Entanglement and Shared Quantum States Geometric Measure of Entanglement and Shared Quantum States

2008-03-07

arxiv.org/abs/0803.1040v2

Phys. Rev. A 78, 032304(2008)(8 pages)

Physics

Quantum Physics

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

Scientific paper

10.1103/PhysRevA.78.032304

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.

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