# On the geometry of entangled states

@article{Verstraete2001OnTG, title={On the geometry of entangled states}, author={F. Verstraete and Jeroen Dehaene and Bart De Moor}, journal={Journal of Modern Optics}, year={2001}, volume={49}, pages={1277 - 1287} }

The basic question that is addressed in this paper is finding the closest separable state for a given entangled state, measured with the Hilbert-Schmidt distance. While this problem is in general very difficult, we show that the following strongly related problem can be solved: find the Hilbert-Schmidt distance of an entangled state to the set of all partially transposed states. We prove that this latter distance can be expressed as a function of the negative eigenvalues of the partial…

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