We present an educational activity for measuring Wigner distribution functions of quantum states of light in the undergraduate laboratory. The activity was implemented by undergraduate students in different courses of the undergraduate curriculum, and the resulting activity was tested by different students of an introductory Quantum Optics course at the Universidad de los Andes in Bogotá, Colombia. The activity consists of a two-hour laboratory practice where students work in a pre-aligned experimental setup and then use an open-access, custom made computational graphical user interface that enables the reconstruction of the Wigner distribution function. Since the testing of the activity coincided with the COVID-19 pandemic, the possibility of analyzing simulated data was included in the computational user interface. The activity is now running for in-person classes and its virtual feature is now valuable for the implementation of distance learning of Quantum Optics.
We present an educational activity for measuring Wigner distribution functions of quantum states of light in the undergraduate laboratory. The activity was implemented by undergraduate students in different courses of the undergraduate curriculum, and the resulting activity was tested by different students of an introductory Quantum Optics course at the Universidad de los Andes in Bogotá, Colombia. The activity consists of a two-hour laboratory practice where students work in a pre-aligned experimental setup and then use an open-access, custom made computational graphical user interface that enables the reconstruction of the Wigner distribution function. Since the testing of the activity coincided with the COVID-19 pandemic, the possibility of analyzing simulated data was included in the computational user interface. The activity is now running for in-person classes and its virtual feature is now valuable for the implementation of distance learning of Quantum Optics.
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.
We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and configure a variety of different optical experiments, while the runtime environment provides unique capabilities for visualization and analysis. All standard linear optical components are available as well as sources of thermal, coherent, and entangled Gaussian states. A unique aspect of VQOL is the introduction of non-Gaussian measurements using detectors modeled as deterministic devices that "click" when the amplitude of the light falls above a given threshold. We describe the underlying theoretical models and provide some illustrative examples. We find that VQOL provides a faithful representation of many experimental quantum optics phenomena and may serve as both a useful instructional tool for students as well as a valuable research tool for practitioners.
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.
In this work, a continuous variable quantum tomography is presented. This is done using two approaches, one using simulated data and another one using data from measurements performed in the laboratory. The Radon inverse transform, under the approximation of filtered back projection, alongside the details on the implementa- tion of balanced homodyne detection needed to perform the tomography are clearly explained. Density matrices in the quadrature and number representation are also obtained from the Wigner function. Additionally, complete documentation of the computational implementation and a user-friendly interface for the tomography is reported
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.