Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1910.07845 · European Journal of Physics

Encrypt me! A game-based approach to Bell inequalities and quantum cryptography

Andrea López-Incera, Andreas Hartmann, Wolfgang Dür

Published Jun 8, 2020• 23 citations
arXivHTMLPDF

Abstract

Abstract Recent progress in the development of quantum technologies, most notably in the context of quantum computing and cryptography, poses the question of whether and how to teach the modern and sophisticated underlying theory of quantum physics, and its applications, at school. To this end, we present a game-based approach to teach Bell inequalities and quantum cryptography at undergraduate level. The approach is based on kinesthetic activities and allows students to experience and discover quantum features and their applications first-hand. The students obtain the same results as if they were in a real laboratory performing sophisticated experiments such as Bell tests, without requiring expensive tools and facilities. Specifically, quantum states are represented by the orientation of students, who also play the role of quantum particles, and mimic quantitative random behaviour and measurements using dice and apps.

DOI
10.1088/1361-6404/ab9a67

Related papers

Entangle me! A game to demonstrate the principles of quantum mechanics

Andrea López-Incera, Wolfgang Dür

We introduce a game to illustrate the principles of quantum mechanics using a qubit (or spin-first) approach, where students can experience and discover its puzzling features first-hand. Students play the role of particles and scientists. Scientists unravel underlying rules and properties by collecting and analysing data that are generated by observing particles that act according to the given rules. We show how this allows one to illustrate quantum states and their stochastic behavior under measurements as well as quantum entanglement. In addition, we use this approach to illustrate and discuss decoherence and a modern application of quantum features, namely, quantum cryptography. We have tested the game in the class and report on the results that we obtained.

arXiv:1901.07587•American Journal of Physics•Jan 17, 2019•30 citations

From probabilities to Bell’s inequalities: a pathway for secondary school quantum literacy

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

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.

Journal of Physics Conference Series•Mar 1, 2026•0 citations

Teaching quantum mechanics in secondary schools: A qubit-first learning path to Bell's inequalities

Alberto Carlini, Andrea Lanza, Dalida Monti +5 more

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.

physics.ed-phCross-listedarXiv:2610.29834•Oct 22, 2026•0 citations

Formal and informal approaches to quantum mechanics using quantum cryptography

Maria Bondani, Valentina De Renzi

Abstract Quantum technologies rely on superposition and entanglement, concepts that challenge classical physics and provide a rich context for teaching. In this paper, we report on a course for high school teachers that focused on quantum cryptography, one of the most mature quantum technologies. The course aims to provide teachers with an innovative approach to introducing quantum physics at the high-school level, showcasing quantum cryptography as a compelling example of how modern technology exploits fundamental principles of quantum theory. The course covers quantum mechanics, light polarization, and the BB84 quantum key distribution protocol through theoretical and experimental sessions by integrating formal and informal approaches exploiting lectures, online simulations (QuVis) and hands-on laboratory activities (using Thorlabs Quantum Cryptography Demonstration Kit). In addition, a card game, originally developed as a public outreach tool, was introduced to interactively perform the BB84 protocol. Feedback from teachers confirmed the feasibility of integrating these concepts into curricula to promote quantum literacy and engagement in secondary education.

Journal of Physics Conference Series•Aug 1, 2026•0 citations

Simulating Bell inequalities with Qibo

Isabella Masina, Giuseppe Lo Presti, Matteo Robbiati +1 more

Abstract We present educational material about Bell inequalities in the context of quantum computing. In particular, we provide software tools to simulate their violation, together with a guide for classroom discussion. The material is organized in three modules of increasing difficulty, and the relative implementation has been written in Qibo, an open-source software suite to simulate quantum circuits with the ability to interface with quantum hardware. The topic of inequalities allows us to not only introduce undergraduate or graduate students to crucial theoretical issues in quantum mechanics, such as entanglement, correlations, hidden variables and non-locality, but also to practically put hands on tools to implement a real simulation, where statistical aspects and noise coming from current quantum chips also come into play.

arXiv:2501.01434•European Journal of Physics•Apr 15, 2025•0 citations

An instrument-free demonstration of quantum key distribution for high-school students

María José Carreño, Jonathan Sepúlveda, Silvia Tecpan +2 more

Abstract It has become increasingly common for high-school students to see media reports on the importance of quantum mechanics in the development of next-generation industries such as drug development and secure communication, but few of them have been exposed to fundamental quantum mechanical concepts in a meaningful classroom activity. In order to bridge this gap, we design and implement a low-cost 20 min demonstration of the Bell test, which is used in several entanglement-based quantum key distribution protocols. The demonstration introduces ideas such as the quantum state, quantum measurement, spin quantization, cryptography, and entanglement; all without using concepts beyond the 9th grade of the Chilean high-school curriculum. The demonstration can serve to promote early exposure of the future adopters and developers of quantum technology with its conceptual building blocks, and also to educate the general public about the importance of quantum mechanics in modern industry.

arXiv:1904.10537•Physics Education•Aug 29, 2019•8 citations
Abstract Recent progress in the development of quantum technologies, most notably in the context of quantum computing and cryptography, poses the question of whether and how to teach the modern and sophisticated underlying theory of quantum physics, and its applications, at school. To this end, we present a game-based approach to teach Bell inequalities and quantum cryptography at undergraduate level. The approach is based on kinesthetic activities and allows students to experience and discover quantum features and their applications first-hand. The students obtain the same results as if they were in a real laboratory performing sophisticated experiments such as Bell tests, without requiring expensive tools and facilities. Specifically, quantum states are represented by the orientation of students, who also play the role of quantum particles, and mimic quantitative random behaviour and measurements using dice and apps.
We introduce a game to illustrate the principles of quantum mechanics using a qubit (or spin-first) approach, where students can experience and discover its puzzling features first-hand. Students play the role of particles and scientists. Scientists unravel underlying rules and properties by collecting and analysing data that are generated by observing particles that act according to the given rules. We show how this allows one to illustrate quantum states and their stochastic behavior under measurements as well as quantum entanglement. In addition, we use this approach to illustrate and discuss decoherence and a modern application of quantum features, namely, quantum cryptography. We have tested the game in the class and report on the results that we obtained.
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.
Abstract Quantum technologies rely on superposition and entanglement, concepts that challenge classical physics and provide a rich context for teaching. In this paper, we report on a course for high school teachers that focused on quantum cryptography, one of the most mature quantum technologies. The course aims to provide teachers with an innovative approach to introducing quantum physics at the high-school level, showcasing quantum cryptography as a compelling example of how modern technology exploits fundamental principles of quantum theory. The course covers quantum mechanics, light polarization, and the BB84 quantum key distribution protocol through theoretical and experimental sessions by integrating formal and informal approaches exploiting lectures, online simulations (QuVis) and hands-on laboratory activities (using Thorlabs Quantum Cryptography Demonstration Kit). In addition, a card game, originally developed as a public outreach tool, was introduced to interactively perform the BB84 protocol. Feedback from teachers confirmed the feasibility of integrating these concepts into curricula to promote quantum literacy and engagement in secondary education.
Abstract We present educational material about Bell inequalities in the context of quantum computing. In particular, we provide software tools to simulate their violation, together with a guide for classroom discussion. The material is organized in three modules of increasing difficulty, and the relative implementation has been written in Qibo, an open-source software suite to simulate quantum circuits with the ability to interface with quantum hardware. The topic of inequalities allows us to not only introduce undergraduate or graduate students to crucial theoretical issues in quantum mechanics, such as entanglement, correlations, hidden variables and non-locality, but also to practically put hands on tools to implement a real simulation, where statistical aspects and noise coming from current quantum chips also come into play.
Abstract It has become increasingly common for high-school students to see media reports on the importance of quantum mechanics in the development of next-generation industries such as drug development and secure communication, but few of them have been exposed to fundamental quantum mechanical concepts in a meaningful classroom activity. In order to bridge this gap, we design and implement a low-cost 20 min demonstration of the Bell test, which is used in several entanglement-based quantum key distribution protocols. The demonstration introduces ideas such as the quantum state, quantum measurement, spin quantization, cryptography, and entanglement; all without using concepts beyond the 9th grade of the Chilean high-school curriculum. The demonstration can serve to promote early exposure of the future adopters and developers of quantum technology with its conceptual building blocks, and also to educate the general public about the importance of quantum mechanics in modern industry.