Tuesday, August 6, 2013

1308.0806 (Lin Chen et al.)

A comparison of old and new definitions of the geometric measure of

Lin Chen, Martin Aulbach, Michal Hajdusek
Several inequivalent definitions of the geometric measure of entanglement (GM) have been introduced and studied in the past. Here we review five known definitions and introduce two new definitions, with the qualifying criterion being that for pure states the measure is a linear or logarithmic function of the maximal fidelity with product states. The entanglement axioms and properties of the measures are studied, and qualitative and quantitative comparisons are made between all definitions. Streltsov et al. [New J. Phys 12 123004 (2010)] proved the equivalence of two linear definitions of GM, whereas we show that the corresponding logarithmic definitions are distinct. Certain classes of states such as "maximally correlated states" and isotropic states are particularly valuable for this analysis. One of the newly introduced GM definition is found to be the first one to be both normalized and weakly monotonous, thus being a prime candidate for future studies of multipartite entanglement. We also find that a large class of graph states, which includes all cluster states, have a "universal" closest separable state that minimizes the quantum relative entropy, the Bures distance and the trace distance.
View original: http://arxiv.org/abs/1308.0806

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