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Complex multi-projective variety and entanglement

Hoshang Heydari·Gunnar Björk
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Abstract

In this paper, we will show that a vanishing generalized concurrence of a separable state can be seen as an algebraic variety called the Segre variety. This variety define a quadric space which gives a geometric picture of separable states. For pure, bi- and three-partite states the variety equals the generalized concurrence. Moreover, we generalize the Segre variety to a general multipartite state by relating to a quadric space defined by two-by-two subdeterminants.

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Hoshang Heydari, Gunnar Björk. 2004-12-07. Complex multi-projective variety and entanglement. https://arxiv.org/abs/quant-ph/0412051

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