Completely mixed state is a critical point for three-qubit entanglement

Details Completely mixed state is a critical point for three-qubit entanglement Completely mixed state is a critical point for three-qubit entanglement

2010-10-14

arxiv.org/abs/1010.2848v3

Phys. Lett. A 375, 2224-2229 (2011)

Physics

Quantum Physics

two references are added, reshaped, few points are clarified

Scientific paper

10.1016/j.physleta.2011.04.056

Pure three-qubit states have five algebraically independent and one algebraically dependent polynomial invariants under local unitary transformations and an arbitrary entanglement measure is a function of these six invariants. It is shown that if the reduced density operator of a some qubit is a multiple of the unit operator, than the geometric entanglement measure of the pure three-qubit state is absolutely independent of the polynomial invariants and is a constant for such tripartite states. Hence a one-particle completely mixed state is a critical point for the geometric measure of entanglement.

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