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arXiv:quant-ph/0703005

Toric varieties: Simple combinatorial and geometrical structure of multipartite quantum systems

Hoshang Heydari

Published Mar 1, 2007• 0 citations
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Abstract

We investigate the geometrical structure of multipartite states based on the construction of toric varieties. We show that the toric variety represents the space of general pure states and projective toric variety defines the space of separable set of multi-qubits states. We also discuss in details the construction of single-, two-, three-, and multi- qubits states. This construction gives a very simple and elegant visual representation of the geometrical structure of multipartite quantum systems.

DOI
10.48550/arxiv.quant-ph/0703005

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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.
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