Geometric measures of entanglement and the Schmidt decomposition

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dc.creatorOstapchuk, D.
dc.creatorPassante, G.
dc.creatorKobes, R.
dc.creatorKunstatter, G.
dc.date2007-07-26
dc.date2007-09-09
dc.date.accessioned2026-07-07T08:28:01Z
dc.date.available2026-07-07T08:28:01Z
dc.descriptionIn the standard geometric approach to a measure of entanglement of a pure state, $\sin^2θ$ is used, where $θ$ is the angle between the state to the closest separable state of products of normalized qubit states. We consider here a generalization of this notion to separable states consisting of products of unnormalized states of different dimension. In so doing, the entanglement measure $\sin^2θ$ is found to have an interpretation as the distance between the state to the closest separable state. We also find the components of the closest separable state and its norm have an interpretation in terms of, respectively, the eigenvectors and eigenvalues of the reduced density matrices arising in the Schmidt decomposition of the state vector.
dc.description7 pages, latex, 1 figure; changed emphasis to Schmidt decomposition
dc.identifierhttps://arxiv.org/abs/0707.4020
dc.identifierhttp://arxiv.org/abs/0707.4020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137470
dc.subjectQuantum Physics
dc.titleGeometric measures of entanglement and the Schmidt decomposition
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