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Quantum Information Processing

, Volume 7, Issue 1, pp 43–50 | Cite as

Geometrical Structure of Entangled States and the Secant Variety

  • Hoshang Heydari
Article

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.

Keywords

multipartite quantum system quantum entanglement complex projective variety secant variety of the serge variety 

PACS

03.65.Ta 03.65.Ud 03.67.Mn 02.40.Dr 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institute of Quantum ScienceNihon UniversityChiyoda-ku, TokyoJapan

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