Abstract The teaching of quantum technologies has now become a leading topic and is at the heart of numerous international programs (e.g., quantum flagship, National Quantum Initiative, UK national quantum technology program) with the aim of widening the workforce and preparing the next generations of experts. In the present contribution, we present an approach for teaching the Second Quantum Revolution to secondary school students that we developed in recent years. The approach aims to emphasize the ongoing revolution as first of all a cultural revolution and its intrinsic interdisciplinary character. As an emblematic case of some aspects of the approach, we present an activity on the classical and quantum random walk algorithms whose main aims are to recontextualize some basic quantum concepts (quantum state, state manipulation/evolution, measurement, and entanglement) in the case of the algorithm and to reflect on the main differences between the classical and quantum case in terms of logic behind its functioning as well as from an epistemological perspective.
Abstract The teaching of quantum technologies has now become a leading topic and is at the heart of numerous international programs (e.g., quantum flagship, National Quantum Initiative, UK national quantum technology program) with the aim of widening the workforce and preparing the next generations of experts. In the present contribution, we present an approach for teaching the Second Quantum Revolution to secondary school students that we developed in recent years. The approach aims to emphasize the ongoing revolution as first of all a cultural revolution and its intrinsic interdisciplinary character. As an emblematic case of some aspects of the approach, we present an activity on the classical and quantum random walk algorithms whose main aims are to recontextualize some basic quantum concepts (quantum state, state manipulation/evolution, measurement, and entanglement) in the case of the algorithm and to reflect on the main differences between the classical and quantum case in terms of logic behind its functioning as well as from an epistemological perspective.
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.
We describe the development of a course of quantum mechanics for secondary school designed to address the challenges related to the revision of classical knowledge, to the building of a well-organized knowledge structure on the discipline, and to the development of a plausible picture of the quantum world. The course is based on a systemic approach to conceptual change, which relies on its analysis in the transition from classical to quantum mechanics, and coordinates cognitive and epistemological aspects. We show how our approach drives the derivation of design principles, how these principles guide the development of the instructional sequence and of its strategies, how their implementation requires the blending of different research perspectives and learning systems. The first challenge is addressed through a path of revision of classical concepts and constructs which leverages prior knowledge according to the dynamics of each notion in theory change. The second by adopting a framework that promotes the construction of a unifying picture of quantum measurement across contexts. The third by designing the course around a modelling process that engages students in epistemic practices of the theoretical physicist, such as generating and/or running thought experiments, and mathematical modelling in a purely theoretical setting. All is aimed to help students accept the quantum description of the world as a plausible product of their own inquiry. This process is assisted by the discussion of the facets of the foundational debate that are triggered by each of the suggested interpretive choices, with the goal to promote an awareness of its cultural significance, of the limits the chosen stance, of the open issues. Data on the cycles of refinement illustrate how a set of activities have been made effective in addressing the challenges at a local level.
This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counter-intuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from
Quantum mechanics (QM) has taken on a paradigmatic role in how physics describes and builds new knowledge about the world. It also has a growing role in our society thanks to recent and rapid developments in the field of new quantum technologies. These are becoming increasingly important in our society, in the world of work and which will also decisively influence future socio-economic choices. Also for this reason QM has an increasing role in the education of young people and has been introduced in many different ways also in secondary school in all continents. The change in the theoretical and cultural frame has profound implications that are often not intuitive, which involve the appropriation of a specific way of thinking. Neither macroscopic phenomenology, nor intuition help, because there is no simple evidence of how quantum objects must be thought to interpret that unobservable microscopic world and for which we must enter another interpretative paradigm even if we want to limit ourselves to describe it. PER has carried out several studies on the learning of key concepts, on the learning nodes, the ways of reasoning, the difficulties of the students, their spontaneous ideas, according to two main strands: above all at university level, conceptual difficulties and misunderstandings often linked to a formal approach, which, moreover, underpins the very nature of the entities involved; at secondary school level in relation to how students acquire a quantum view of phenomena on the basis of specific approaches adopted to address QM. In particular, a vast literature, which has increased considerably and especially in relatively recent times, has studied how university students deal with certain concepts such as that of state, superposition, measurement in quantum mechanics rather than how quantum quantities evolve over time. These studies are based on the use of questionnaires that allow to explore different levels: the verbal, formal and representative one, with different representations (eg. wave function, Dirac notation), rather than different representative modes (eg. Graphs of probability amplitudes, or probability distributions). At the secondary school level, the most important studies on student learning were instead conducted evaluating the educational impact and outlining the learning paths of students who had followed formative activities based on differentiated innovative research-based educational paths. In particular, the learning outcomes were compared to those activated by proposals based on the historical reconstruction approach of quantum physics. This approach is privileged in traditional curricula and school texts and consequently in the ways of teachers approaching the topic. It was developed in schools with a narrative or descriptive dimension of solutions based on old physics of quanta for the interpretation of phenomena not explained by classical physics. The innovative approaches instead make use of contexts whose formal treatment is simple (quantum properties described in a two-state space such as polarization or spin) with the aid of simulations that compensate for the problem of students” limited mathematical-formal skills, avoiding any historical reference. In particular, there is a significant difference between the survey tools and the survey contexts in the high school environment compared to surveys conducted with university students. This paper presents a review of the research literature, focusing in particular on the learning processes of secondary school students and outlining how research perspectives have evolved.
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 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.