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.
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Heydari, H. Geometrical Structure of Entangled States and the Secant Variety. Quantum Inf Process 7, 43–50 (2008). https://doi.org/10.1007/s11128-007-0071-4
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DOI: https://doi.org/10.1007/s11128-007-0071-4
Keywords
- multipartite quantum system
- quantum entanglement
- complex projective variety
- secant variety of the serge variety