Geometrical Structure of Entangled States and the Secant Variety

Authors:
Hoshang Heydari
Affiliations:
Institute of Quantum Science, Nihon University, Chiyoda-ku, Tokyo, Japan 101-8308
Venue:
Quantum Information Processing
Year:
2008

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On invariant notions of Segre varieties in binary projective spaces

Designs, Codes and Cryptography

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Abstract

We investigate the geometrical structure of entangled and separable bipartite and multipartite states based on the secant variety of the Segre variety. We show that the Segre variety coincides with the space of separable multipartite state and the higher secant variety of the Segre variety coincides with the space of entangled multipartite states.