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arXiv:1112.3754 · Journal of Physics Conference Series

Geometrical structures of multipartite quantum systems

Hoshang Heydari

Published Feb 8, 2012• 0 citations
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Abstract

In this paper I will investigate geometrical structures of multipartite quantum systems based on complex projective varieties. These varieties are important in characterization of quantum entangled states. In particular I will establish relation between multi-projective Segre varieties and multip-qubit quantum states. I also will discuss other geometrical approaches such as toric varieties to visualize complex multipartite quantum systems.

DOI
10.1088/1742-6596/343/1/012045

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In this paper I will investigate geometrical structures of multipartite quantum systems based on complex projective varieties. These varieties are important in characterization of quantum entangled states. In particular I will establish relation between multi-projective Segre varieties and multip-qubit quantum states. I also will discuss other geometrical approaches such as toric varieties to visualize complex multipartite quantum systems.
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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.
In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi‐qubit states in terms of these schemes and also discuss separability and entanglement of bipartite and multipartite quantum states. These results give some geometrical insight to the fascinating quantum mechanical phenomena of entanglement which is fundamentally important and has many applications in the field of quantum computing.
In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi‐qubit states in terms of these schemes and also discuss separability and entanglement of bipartite and multipartite quantum states. These results give some geometrical insight to the fascinating quantum mechanical phenomena of entanglement which is fundamentally important and has many applications in the field of quantum computing.