Geometric measures of entanglement and the Schmidt decomposition

Details Geometric measures of entanglement and the Schmidt decomposition Geometric measures of entanglement and the Schmidt decomposition

2007-07-26

arxiv.org/abs/0707.4020v2

Physics

Quantum Physics

7 pages, latex, 1 figure; changed emphasis to Schmidt decomposition

Scientific paper

In the standard geometric approach to a measure of entanglement of a pure state, $\sin^2\theta$ is used, where $\theta$ 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 $\sin^2\theta$ 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.

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