This paper presents an innovative experiment and theoretical framework designed for senior-level undergraduate students to explore quantum state tomography and Bell inequality tests. The experiment utilizes pulsed laser light and a carefully engineered optical system to emulate quantum entanglement, enabling students to investigate foundational quantum phenomena using accessible laboratory tools. Through practical measurements and simulations, students reconstruct quantum states and analyze correlations indicative of entanglement and non-locality. The setup includes polarization analysis across multiple measurement bases and culminates in the measurement of Bell’s parameter using the CHSH test. By combining experimental emulation with computational analysis, this approach provides a compelling educational bridge between abstract quantum theory and hands-on experiments, highlighting the conceptual and practical relevance of quantum entanglement in modern physics.
This paper presents an innovative experiment and theoretical framework designed for senior-level undergraduate students to explore quantum state tomography and Bell inequality tests. The experiment utilizes pulsed laser light and a carefully engineered optical system to emulate quantum entanglement, enabling students to investigate foundational quantum phenomena using accessible laboratory tools. Through practical measurements and simulations, students reconstruct quantum states and analyze correlations indicative of entanglement and non-locality. The setup includes polarization analysis across multiple measurement bases and culminates in the measurement of Bell’s parameter using the CHSH test. By combining experimental emulation with computational analysis, this approach provides a compelling educational bridge between abstract quantum theory and hands-on experiments, highlighting the conceptual and practical relevance of quantum entanglement in modern physics.
The growth of quantum technologies is attracting the interest of many students eager to learn concepts such as quantum entanglement or quantum superposition. However, the non-intuitive nature of these concepts poses a challenge to understanding them. Here, we present an entangled photon system which can perform a Bell test, i.e. the CHSH inequality, and can obtain the complete tomography of the two-photon state. The proposed setup is versatile, cost-effective and allows for multiple classroom operating modes. We present two variants, both facilitating the measurement of Bell inequalities and quantum state tomography. Experimental results showcase successful manipulation of the quantum state of the photons, achieving high-fidelity entangled states and significant violations of Bell's inequalities. Our setup's simplicity and affordability enhances accessibility for less specialized laboratories, allowing students to familiarize themselves with quantum physics concepts.
Abstract This paper presents a new lab work concept promoting a series of quantum optics experiments: experimental milestones on the quantum behaviour of light designed for undergraduate lab work. The experiments may be carried out with considerably less effort while addressing the fundamentals of quantum theory: quantum states and their superposition, detected via the propagation phase of probability amplitudes; quantum nonlocality, detected via the change of the state due to localized detection; quantum entanglement , detected via the violation of Bell ’s inequality (CHSH criterion). The experimental setup is designed to meet the requirements of barrier-free multilevel use in undergraduate physics lab courses: students’ labs for secondary school students, undergraduate university labs for physics students (science and science education) and lab work assisted courses for the training of in-service physics teachers. This article is aimed to describe the basics of the setup and to show how the experiments may be implemented into lab courses to match different educational course levels. The experimental series could prove to be promising in terms of fruitful discussion of quantum theory fundamentals without semiclassical pitfalls.
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.
Teaching quantum mechanics is challenging, not least because the theory often conflicts with our classical worldview. Quantum correlations in particular are notoriously counter-intuitive. Their non-classical behavior is typically revealed through Bell-type inequalities. Among these, Wigner's Inequality constitutes a particularly accessible test, as it relies on minimal set-theoretic assumptions. In this pedagogical paper, we derive Wigner's Inequality, describe a quantum-optical setup to experimentally violate it, and provide access to the raw data, enabling students and instructors to perform their own analyses. Our measured data shows clear violations of Wigner's Inequality, directly illustrating the non-classical nature of quantum correlations. By connecting theory, experiment, and data analysis, this paper equips educators with a resource for engaging students in authentic scientific practice and developing a deeper understanding of quantum systems.
Quantum cryptography remains a topic of enduring scientific and educational interest. Here, we present a clear and accessible framework for exploring the six-state quantum key distribution protocol, an enhanced three-basis extension of the BB84 scheme that combines optical experiments with computational analysis. Designed for testing quantum communication protocols through emulation, this approach provides a robust and cost-effective platform that highlights the fundamental principles of multi-basis encoding and demonstrates how experimental measurements connect directly to theoretical expectations in a controlled tabletop setting.
Abstract A laboratory experiment and related computational activities for advanced undergraduate or introductory graduate students on quantum entanglement are developed and described. Students characterize the quality of entanglement of a system, use code to predict the best experimental parameters for the system, and then perform a modified Bell measurement. The results can show non-classical behavior for any (non-zero) level of entanglement. Demonstration of the experiment on an IBM quantum computer is also shown, including the additional effects of decoherence on such a system. While a potentially interesting experiment for any program, it can open new avenues of education particularly for smaller colleges and universities on a more limited budget.