Exploring the mechanisms of qubit representations and introducing a new category system for visual representations: Results from expert ratings

Abstract: In quantum physics (QP) education, the use of representations such as diagrams and visual aids that connect to mathematical concepts is crucial. Research in representation theory indicates that combining symbolic-mathematical elements (e.g. formulae) with visual-graphical representations enhances conceptual understanding more effectively than representations that merely depict phenomena. However, common representations vary widely, and existing categorisation systems do not adequately distinguish between them in QP. To address this, we developed a new set of differentiation criteria based on insights from representation research, QP education, and specific aspects of the quantum sciences. We created a comprehensive category system for evaluating visual QP representations for educational use, grounded in Ainsworths (2006) DeFT Framework. Twenty-one experts from four countries evaluated this category system using four qubit representations: the Bloch sphere, Circle Notation, Quantum Bead, and the pie chart (Qake) model. This evaluation enabled us to assess the discriminative power of our criteria and the effectiveness of each representation in supporting the learning of QP concepts. It evaluated how well each representation conveyed quantum concepts such as quantum state, measurement, superposition, entanglement, and quantum technologies (X-, Z-, and H-gates) across 16 criteria. The results showed significant differences in the effectiveness of these representations, particularly in conveying key concepts like superposition and measurement. Additionally, expert ratings indicated notable variations in the potential of each representation to induce misconceptions, linked to differences in shape, measurement behaviour, and requirements for understanding entanglement. We also discuss considerations for developing new representations and suggest directions for future empirical studies.