Multipartite quantum systems and symplectic toric manifolds

TL;DR

This paper explores the geometric structures of multi-qubit quantum states using symplectic toric manifolds, focusing on entanglement and state space representations through advanced geometric and algebraic tools.

Contribution

It introduces a geometric framework for analyzing multipartite quantum states via symplectic toric manifolds and Delzant's construction, linking quantum information with symplectic geometry.

Findings

Characterization of single-qubit state space as a symplectic toric manifold

Analysis of entangled states using moment maps and toric varieties

Connection between quantum entanglement and geometric structures

Abstract

In this paper we study the geometrical structures of multi-qubit states based on symplectic toric manifolds. After a short review of symplectic toric manifolds, we discuss the space of a single quantum state in terms of these manifolds. We also investigate entangled multipartite states based on moment map and Delzant's construction of toric manifolds and algebraic toric varieties.