A toric varieties approach to geometrical structure of multipartite states

Details A toric varieties approach to geometrical structure of multipartite states A toric varieties approach to geometrical structure of multipartite states

2010-01-19

arxiv.org/abs/1001.3245v1

AIP Conf.Proc, 1232, 283-287, 2010

Physics

Quantum Physics

Talk given at the Vaxjo conference on Quantum Theory: Reconsideration of Foundations-5 (QTRF-5)

Scientific paper

We investigate the geometrical structures of multipartite states based on construction of toric varieties. In particular, we describe pure quantum systems in terms of affine toric varieties and projective embedding of these varieties in complex projective spaces. We show that a quantum system can be corresponds to a toric variety of a fan which is constructed by gluing together affine toric varieties of polytopes. Moreover, we show that the projective toric varieties are the spaces of separable multipartite quantum states. The construction is a generalization of the complex multi-projective Segre variety. Our construction suggests a systematic way of looking at the structures of multipartite quantum systems.

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