Who's afraid of the Unit Quaternion ?

TL;DR

This paper explores the mathematical and geometric nature of qubits, revealing that they are better represented as unit quaternions or spinors on a 3-sphere, providing deeper insight into their global phase.

Contribution

It reinterprets qubits as unit quaternions, connecting quantum states to geometric objects on a 3-sphere, which is a novel perspective in quantum information theory.

Findings

Qubits are equivalent to unit quaternions (spinors).

Quantum states trace paths on the 3-sphere surface.

Global phase corresponds to geometric properties of the 3-sphere.

Abstract

Far from being just a 2-level Quantum system the Qubit is a Unit Quaternion, also known as a Spinor. Therefore it follows that the Qubit is a 4-dimensional vector which traces a path on the surface of the unit 3-sphere. This is the meaning of the global phase.