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The Coin-Flipping Game Paradox: A Pedagogical Introduction to Quantum Computing and Superposition

Xènia Fonoll González

Published May 18, 2026• 0 citations
Publisher

Abstract

This paper introduces fundamental concepts of quantum mechanics and quantum computing through the quantum coin-flipping paradox. By connecting historical developments such as Planck’s quantum hypothesis, wave-particle duality, and the double-slit experiment with modern quantum circuits implemented in Qiskit, the work provides a pedagogical and self-contained introduction to superposition and quantum advantage. The article combines theoretical explanation, experimental demonstrations, and computational implementations to make quantum computing accessible to a broad audience.

DOI
10.5281/zenodo.20268961

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This paper introduces fundamental concepts of quantum mechanics and quantum computing through the quantum coin-flipping paradox. By connecting historical developments such as Planck’s quantum hypothesis, wave-particle duality, and the double-slit experiment with modern quantum circuits implemented in Qiskit, the work provides a pedagogical and self-contained introduction to superposition and quantum advantage. The article combines theoretical explanation, experimental demonstrations, and computational implementations to make quantum computing accessible to a broad audience.
The double-slit experiment provides insights into quantum mechanics and sheds light on fundamental contradictions with classical physics, which, although predicting independent trajectories by simple random addition, reveals interference patterns even when only one particle is emitted at a time, providing direct evidence for effects of wave-particle duality and quantum superposition. Furthermore, we explore why thematic coherence and overlap in this study are essential elements of quantum computer design. Mechanisms such as phase interference (defined by the Deutsch algorithm) demonstrate the computational power provided by quantum effects. In other words, double-slit learning is not just a theoretical concept, but also a set of ideas and techniques that combine the theory of advanced quantum technology.
This educational module provides an accessible introduction to quantum computing and is designed as the first practicum in a broader series. The presentation covers the fundamental concepts required to understand the principles and potential of quantum computation, including qubits, superposition, entanglement, decoherence, quantum gates, the Bloch sphere, and measurement. It also introduces current hardware platforms such as superconducting, trapped‑ion, and photonic qubits. The module explains the structure of quantum circuits, the role of unitary operations, and the significance of quantum parallelism and quantum advantage. It includes visual metaphors (such as Schrödinger’s cat), conceptual diagrams, and examples of real-world quantum processors. The presentation also addresses common misconceptions about quantum computers and outlines ethical, social, and educational challenges associated with the development of quantum technologies. Version 0.3 includes improved structure, updated terminology, expanded explanations of quantum gates, and a fully revised English-language adaptation suitable for international audiences. The material is intended for students, educators, and early‑stage researchers entering the field of quantum information science.
From the Publisher: This book aims to provide a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation as well as some experimental aspects of quantum computation and quantum cryptography. Only knowledge of basic quantum mechanics is assumed. Whenever more advanced concepts and techniques are used, they are introduced carefully. This book is meant to be a self-contained overview. While basic concepts are discussed in detail, unnecessary technical details are excluded. It is well-suited for a wide audience ranging from physics graduate students to advanced researchers.
Quantum computing represents a transformative approach to computation by leveraging the fundamental principles of quantum mechanics. Unlike classical computing, which operates on bits, quantum computing uses quantum bits or qubits that exist in superposition, enabling parallel processing of information. This paper introduces the foundational concepts of quantum computing—such as superposition, entanglement, and quantum gates—and explores how these principles differ from classical models. Further, it highlights the implications of quantum computing in modern physics, especially in areas like quantum simulation, cryptography, and quantum field theory. By avoiding complex mathematical derivations, this paper aims to make quantum computing accessible to a broader academic audience, emphasizing both theoretical insights and practical impacts.
Quantum computing (QC) is a radically new approach to computation. Classical computing is based on the idea of bits: strings of 1's and 0's on which we do arithmetic operations. QC, however, is based on quantum bits, qubits, and new physical operations. Despite the complexity of QC, we contend that it is an appropriate and useful topic for undergraduate physics students. In this talk, we present our results from three small QC projects relating to flipping coins. In the first, we investigate the results of a secret coin flip and use QC to guess whether the coin landed on heads or tails. In the second, we determine whether a given coin is fair or unfair using only a single qubit ( instead of multiple bits). In the third, we explore how quantum communication can alleviate dishonest player biases in coin flipping cryptographic primitives.
Abstract The double-slit experiment is a classic experiment that presents the clearest manifestation of wave-particle duality, one of the fundamental principles of quantum mechanics. The double-slit experiment still remains the phenomenon that demonstrates wave-particle duality at the most fundamental level. This phenomenon quantitatively and conceptually demonstrates that microscopic objects can behave like both waves and particles at the same time. This article provides an in-depth analysis of the physical nature of dualism, the mechanism of formation of the interference pattern, and the impact of the act of observation on the dynamics of quantum systems. The need for a new perspective on this topic is due to the fact that the current uncertainty in the interpretation of quantum reality has not yet been completely eliminated, and the boundaries between classical and quantum behavior in microscopic objects are still being explored. The results presented here restructure the deep mechanisms of the interference picture, more clearly frame the relationship between observation and wavefunction collapse, and provide a quantum. Since the article attempts to provide a complete answer to the mechanism of the formation of wave-particle duality, extensive space is given to sections such as historical development, theoretical models, modern research, etc. New approaches to this phenomenon have been developed using modern research and string theory. As a result, a new mathematical expression has been proposed that explains the reasons for the initial emergence of wave-particle duality, and is also important for string theory. The article explains the measurement problem with a more effective physical structure and ontological model.