The spinorial ball (II): A manipulable qubit at human scale

Abstract

The spinorial ball is an interactive electronic device that we recently introduced to discuss the origin of spin-1/2 from the representation of the rotation group, without the framework quantum mechanics. Nevertheless, it can also be viewed as a macroscopic visualization of a quantum two-level system, and can thus be used to gain intuition on some generic features of qubits. In this article, we show how the ball can be used to fully visualize the evolution of a single qubit under arbitrary operators of SU(2). The Bloch sphere, the Hopf fibration, and the Berry phase can also be easily visualized and manipulated using this original device. We also discuss how the spinorial ball can be used to represent Hamiltonian evolution, and we describe an explicit mapping between the ball's motion and the evolution of a spin-1/2 system in arbitrary magnetic fields. An electronic implementation of projective measurement that matches the predictions of quantum mechanics is also proposed.