This paper proposes a research program aimed at exploring the possibility of establishing a rigorous mathematical foundation for quantum information ontology. We systematically study the path of incorporating the entanglement structure of κ-qubit networks into an extended set-theoretic framework. Based on the principles of Jiuzhang Constructive Math ematics (JCM), we explore the conceptual foundations of constructing a Quantum Informa tion Set Theory (QIST). This paper provides an in-depth analysis of the mathematical and physical challenges faced by this attempt, establishes close connections with fields such as quantum logic, Boolean-valued models, categorical quantum mechanics, and the holographic principle, and proposes a roadmap for its gradual realization. We pay special attention to the dual role of the κ parameter (as a mathematical scale parameter and a physical constant) and its key role in connecting mathematical structures with physical reality. Although a complete theory has not yet been established, this paper provides a systematic research framework and a clear direction for the mathematical rigorization of quantum information ontology.
This paper proposes a research program aimed at exploring the possibility of establishing a rigorous mathematical foundation for quantum information ontology. We systematically study the path of incorporating the entanglement structure of κ-qubit networks into an extended set-theoretic framework. Based on the principles of Jiuzhang Constructive Math ematics (JCM), we explore the conceptual foundations of constructing a Quantum Informa tion Set Theory (QIST). This paper provides an in-depth analysis of the mathematical and physical challenges faced by this attempt, establishes close connections with fields such as quantum logic, Boolean-valued models, categorical quantum mechanics, and the holographic principle, and proposes a roadmap for its gradual realization. We pay special attention to the dual role of the κ parameter (as a mathematical scale parameter and a physical constant) and its key role in connecting mathematical structures with physical reality. Although a complete theory has not yet been established, this paper provides a systematic research framework and a clear direction for the mathematical rigorization of quantum information ontology.
The rapid growth of quantum information science and technology (QIST) presents unique educational challenges as it brings together students and researchers from many disciplines. This work presents findings from in-depth interviews with leading quantum researchers who are also educators, whose perspectives provide guidance for developing a framework for interdisciplinary QIST teaching and builds on our earlier paper that focused on QIST courses and curricula. We discuss quantum educators’ reflections on three critical aspects of QIST education: (1) the development of a common interdisciplinary language, (2) determining appropriate levels of abstraction and physical detail for diverse student populations from various disciplines, and (3) why students should pursue courses, degrees, and careers in this rapidly evolving field. Our analysis reveals that the emergence of linguistic evolutions such as “qubits” and “measurement bases”, rather than a focus on measurement of physical observables and their corresponding Hermitian operators, has begun to create a unifying framework that transcends disciplinary boundaries. Nevertheless, educators face ongoing challenges in balancing the level of abstractness with physical details as well as mathematical rigor with conceptual accessibility, particularly when teaching foundational QIST courses to an interdisciplinary group of students. The experts emphasize that successful QIST education for an interdisciplinary student body not only requires a shift from traditional quantum mechanics pedagogy for physics majors, but careful consideration of students’ diverse prior conceptual and mathematical foundations overall. They encourage students to pursue QIST related courses, degrees, and careers, highlighting the unique historical opportunity to participate in creating transformative quantum technologies while developing transferable skills for an evolving technological landscape. These findings provide valuable guidance for developing a framework for interdisciplinary QIST teaching especially useful for foundational courses.
This paper aims to provide a systematic meta-theoretical framework for the”Quantum Geometrization” research program. From an epistemological perspective, it clarifies that establishing ”information” as the first principle of physics isnot an arbitrary metaphysical presupposition, but is based on two operationallymeaningful meta-rules: conservation of information distinguishability and finitestep computability of physical processes. This paper argues that these two metarules constitute the boundary conditions that any cognizable and testable physicaltheory must satisfy, and together they define the ”operational window of physicalcognition”. Within this framework, spacetime geometry is interpreted as an emergent phenomenon of information structure in the coarse-graining limit, quantumuncertainty is reinterpreted as an inevitable trade-off between levels of information description, and a series of cosmological parameters are traced back to rigidconstraints of information algebra. This paper further synthesizes the core achievements of the Quantum Geometrization series into a unified ”information dynamics”prediction network, and discusses the framework’s scope of applicability, challenges,and future directions. This study provides an epistemological foundation for thecore proposition ”spacetime emerges from information” and places the QuantumGeometrization program within a falsifiable scientific paradigm.
Distributed Presence Research Program (DP) is an interdisciplinary foundational research program investigating whether physical reality can be more coherently understood in terms of distributed, relational, and phase-structured presence rather than as a collection of fundamentally isolated entities. The program explores the possibility that mass, charge, localization, probability, field structure, quantum behavior, and spacetime organization may be interpreted as emergent modes of response, stabilization, and relational configuration within a deeper ontology of distributed presence. A central aim of the program is to develop an ontological unity in physics by articulating a framework in which the interpretation of physical properties, the ontology of fields, the status of probability, and the conceptual foundations of quantum mechanics can be approached within a common relational structure. In particular, the DP Research Program addresses: the ontology of distributed presence, the emergence of localization, the reinterpretation of mass and charge, phase and response structures, the ontological interpretation of probability, the interpretation of quantum mechanics, spacetime emergence, and the search for ontological unity across physical theory. Rather than presenting itself as a completed physical theory, DP develops a conceptual and exploratory formal framework connecting philosophy of physics, metaphysics of science, quantum foundations, field-theoretic interpretation, and ontological modeling. The program aims to function as an open research platform for conceptual clarification, formal development, and interdisciplinary dialogue on the foundations and unity of physical reality.
The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum measurement theory based on completely positive map-valued measures, a universally valid new formulation of the uncertainty principle for error and disturbance in quantum measurements, the Wigner-Araki-Yanase limit of quantum measurements, the accuracy limit of quantum computing based on conservation laws, and a quantum interpretation based on quantum set theory.
This paper investigates the theoretical foundations and practical implications of quantum entanglement information encoding. Traditional information encoding methods are limited by their reliance on classical physics. We propose a novel approach utilizing quantum entanglement to enhance information security and key distribution, offering a potential paradigm shift in data protection. The core mechanism centers around leveraging the unique properties of entangled particles to facilitate significantly more efficient information transfer and secure key distribution compared to existing techniques. This work explores the mathematical underpinnings of this framework, including the encoding and decoding protocols. The paper demonstrates the potential of this approach through theoretical analysis and explores its strengths and weaknesses. The research highlights the challenges and future directions for further development, emphasizing the need for rigorous mathematical validation and experimental testing. We conclude by outlining the key mathematical contributions and the potential impact of this theory on the field of quantum information.
Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.