arXiv:quant-ph/0412051

Complex multi-projective variety and entanglement

Hoshang Heydari, Gunnar G. Bjork

Published Dec 7, 2004• 0 citations

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.

DOI: 10.48550/arxiv.quant-ph/0412051

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