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arXiv:2502.18543 · EPJ Quantum Technology

From staging to insight: an educational path to understanding Bell’s inequalities

Valentina De Renzi, Matteo G. A. Paris, Maria Bondani

Published Oct 27, 2025• 3 citations
arXivHTMLPDF

Abstract

Quantum Physics is a cornerstone of modern science and technology, yet a comprehensive approach to integrating it into school curricula and communicating its foundations to policymakers, industrial stakeholders, and the general public has yet to be established. In this paper, we discuss the rationale for introducing entanglement and Bell’s Inequalities (BI) to a non-expert audience, and how these topics have been presented in the exhibition “Dire l’indicibile” (“Speaking the unspeakable”), as a part of the Italian Quantum Weeks project. Our approach meets the challenge of simplifying quantum concepts without sacrificing their core meaning, specifically avoiding the risks of oversimplification and inaccuracy. Through interactive activities, including a card game demonstration and the staging of CHSH experiments, participants explore the fundamental differences between classical and quantum probabilistic predictions. They gain insights into the significance of BI verification experiments and the implications of the 2022 Nobel Prize in Physics. Preliminary results from both informal and formal assessment sessions are encouraging, suggesting the effectiveness of this approach.

DOI
10.1140/epjqt/s40507-025-00415-5

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Abstract Quantum mechanics is a key part of modern science and technology, but its complexity makes it challenging to teach it in schools. We suggest a teaching method for secondary schools that focuses on Bell’s inequalities and how they are tested experimentally. Using students’ understanding of statistics and probability, we provide a step-by-step approach. This includes hands-on activities, like a simple card game, and discussions of CHSH experiments, to help students see the differences between classical and quantum probability. Early testing shows promising results, indicating that this method could be effective.
Teaching quantum mechanics at the secondary school level remains a major educational challenge. Traditional historical approaches often present the theory as a sequence of disconnected phenomena, requiring extensive prior knowledge of classical physics before students can appreciate the conceptual structure of quantum physics. In this work, we present the design, implementation, and evaluation of a curriculum based on the two state (qubit first) approach, in which the fundamental postulates of quantum mechanics are introduced through mathematically accessible two level systems and realized with light polarization. The curriculum integrates theoretical instruction, laboratory activities, a coherent progression grounded in the interactive simulations, and inquiry based learning into a coherent pathway that progresses from quantum states and superposition to entanglement and the experimental violation of Bell's inequalities. A distinctive feature of the project is the experimental realization of the violation of Bell's inequalities obtained in a newly established quantum optics laboratory in an Italian high school, where students performed, for the first time in Italy, an authentic Bell test using polarization-entangled photons. The same educational framework was adopted for in service teacher professional development courses. Learning outcomes were evaluated through mixed methods. Preliminary analysis indicates significant improvements in conceptual understanding, confidence in using mathematical formalism, and appreciation of the relationship between theory, experimentation, and the foundations of quantum mechanics. The proposed curriculum shows that two-state formalism and supported by real laboratory experiences enables secondary-school students to engage more meaningfully with both the conceptual foundations of quantum mechanics and their experimental verification.
In the context of the Italian Quantum Weeks initiative, the exhibition "Dire l'indicibile" proposed a journey through the rules of Quantum Mechanics, offering a glimpse at the working principles and potential applications of quantum technologies (QTs).We devised a route to introduce the key concepts of quantum superposition, quantum measurements and evolution, and incompatible observables, by exploiting analogies based on custom-made models and tools.As examples of possible QT applications, we choose to discuss: i) the peculiarities of quantum walks (QW), as compared to classical random walks; ii) quantum cryptography and its applications.Two activities -illustrating the basis of QWs and of the BB84 quantum key distribution protocol-were actively performed by the public.The outcome of a satisfaction survey is extremely positive, encouraging us to explore this approach in different educational contexts.
Abstract Teaching and learning quantum mechanics is one of the most demanding educational and conceptual challenges, in particular in secondary schools where students do not possess an adequate mathematical background to effectively support the description of quantum behaviour. Educational research shows that traditional approaches, generally based on historical and narrative perspectives, are only partially effective. The reason is that they do not address in depth those basic quantum concepts that radically question the fundamentals of classical physics. A research-based educational program has been proposed to two final-year classes of an Italian scientific high school. In order to build the main concepts of quantum mechanics and their formal basic representation via real and simulated experiments, the program uses the light polarization as a context. A quantum game was then integrated in the educational program, to support students’ learning. Their conceptual paths, monitored by means of tutorials and questionnaires, show significant student learning especially on the concept of state and on appropriating the formalism meaning, whereas students more frequently referred to the geometrical vector representation instead of the algebraic-analytic formula. The quantum game has emerged to support intuition and operative experience in distinguishing the foundational concepts of superposition and entanglement.