publication . Article . Preprint . 2010

Geometric measures of entanglement and the Schmidt decomposition

Margaret E. Carrington; R. Kobes; Gabor Kunstatter; D. Ostapchuk; Gina Passante;
Open Access
  • Published: 24 Mar 2010 Journal: Journal of Physics A: Mathematical and Theoretical, volume 43, page 315,302 (issn: 1751-8113, eissn: 1751-8121, Copyright policy)
  • Publisher: IOP Publishing
Abstract
In the standard geometric approach, the entanglement of a pure state is $\sin^2\theta$, where $\theta$ is the angle between the entangled state and the closest separable state of products of normalised qubit states. We consider here a generalisation of this notion by considering separable states that consist of products of unnormalised states of different dimension. The distance between the target entangled state and the closest unnormalised product state can be interpreted as a measure of the entanglement of the target state. The components of the closest product state and its norm have an interpretation in terms of, respectively, the eigenvectors and eigenvalu...
Subjects
arXiv: Quantum Physics
free text keywords: General Physics and Astronomy, Mathematical Physics, Modeling and Simulation, Statistics and Probability, Statistical and Nonlinear Physics, Quantum Physics, Quantum Physics (quant-ph), FOS: Physical sciences, Schmidt decomposition, System of linear equations, State vector, Norm (mathematics), Quantum entanglement, Qubit, Mathematics, Eigenvalues and eigenvectors, Separable state, Pure mathematics
Funded by
NSERC
Project
  • Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)
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