Completely mixed state is a critical point for three-qubit entanglement
arXiv:1010.2848 · doi:10.1016/j.physleta.2011.04.056
Abstract
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.
two references are added, reshaped, few points are clarified
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