Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition

DOI10.1088/1751-8113/44/36/365305zbMATH Open1226.81029arXiv1104.3159OpenAlexW3101068306MaRDI QIDQ3173038

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Publication date: 10 October 2011

Published in: (Search for Journal in Brave)

Abstract: In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this entanglement measure for target states with a large degree of symmetry. We obtain analytic solutions for the extrema of the distance function and solve for the Hessian to show that, up to the action of trivial symmetries, the solutions correspond to local minima of the distance function. In addition, we show that the conditions that determine the extremal solutions for general target states can be obtained directly by parametrizing the product states via their Schmidt decomposition.

Full work available at URL: https://arxiv.org/abs/1104.3159

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