Geometrical structures of multipartite quantum systems

TL;DR

This paper explores the geometric structures of multipartite quantum systems using complex projective varieties, linking algebraic geometry with quantum entanglement characterization and visualizing complex states.

Contribution

It establishes a connection between multi-projective Segre varieties and multi-qubit states, introducing geometric methods to analyze multipartite entanglement.

Findings

Relation between Segre varieties and multi-qubit states

Use of toric varieties for visualization of quantum systems

Geometric characterization of entangled states

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.