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

TL;DR

The paper introduces the spinorial ball as a macroscopic device that visualizes and manipulates quantum two-level system features, providing intuitive understanding of concepts like the Bloch sphere, Berry phase, and Hamiltonian evolution.

Contribution

It extends previous work by demonstrating how the spinorial ball visualizes key quantum phenomena and establishes a precise mapping to qubit dynamics, including measurement implementation.

Findings

Visualization of the Bloch sphere, Hopf fibration, and Berry phase using the device

Explicit mapping between the ball's motion and spin evolution in magnetic fields

Electronic implementation of projective measurement consistent with quantum mechanics

Abstract

The spinorial ball is an electronic manipulable device that we recently introduced to discuss the origin of spin-1/2 from rotations group representation, without relying on the quantum mechanics framework. Nevertheless, it is also a macroscopic visualization of a quantum two-level system, and can thus be used to gain intuition on some generic features of qubits. The present article therefore aims to complement and extend our previous work by discussing how the spinorial ball can be used to visualize quantum mechanics features. The Bloch sphere, the Hopf fibration and the Berry phase can for instance easily be seen and manipulated using this original device. We also discuss how the spinorial ball can be used to visualize Hamiltonian evolution, and we describe an explicit mapping between the ball's motion and the evolution of 1/2-spin in arbitrary magnetic field. An electronic implementation of projective measurement that matches the predictions of quantum mechanics is also proposed. The present article is written as a practical guide to manipulate the ball and establishes the exact correspondence between the spinorial ball and a generic two-level system.