Noncommutative geometrical structures of entangled quantum states

TL;DR

This paper explores the noncommutative geometric structures underlying entangled quantum states, revealing that such states form noncommutative spaces and introducing q-deformed relations, with extensions to multi-qubit systems.

Contribution

It introduces a novel framework linking quantum entanglement to noncommutative geometry, including q-deformations and multi-qubit generalizations.

Findings

Pure entangled states form noncommutative spaces

Rewritten conifold and Segre variety yield q-deformed relations

Detailed analysis of three-qubit noncommutative geometry

Abstract

We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewritten the conifold or the Segre variety we can get a $q$-deformed relation in noncommutative geometry. We generalized our construction into a multi-qubit state. We also in detail discuss the noncommutative geometrical structure of a three-qubit state.