An Extended Epistemic Framework Beyond Probability for Quantum Information Processing with Applications in Security, Artificial Intelligence, and Financial Computing
In this work, we propose a novel quantum-informed epistemic framework that extends the classical notion of probability by integrating plausibility, credibility, and possibility as distinct yet complementary measures of uncertainty. This enriched quadruple (P, Pl, Cr, Ps) enables a deeper characterization of quantum systems and decision-making processes under partial, noisy, or ambiguous information. Our formalism generalizes the Born rule within a multi-valued logic structure, linking Positive Operator-Valued Measures (POVMs) with data-driven plausibility estimators, agent-based credibility priors, and fuzzy-theoretic possibility functions. We develop a hybrid classical-quantum inference engine that computes a vectorial aggregation of the quadruples, enhancing robustness and semantic expressivity in contexts where classical probability fails to capture non-Kolmogorovian phenomena such as entanglement, contextuality, or decoherence. The approach is validated through three real-world application domains-quantum cybersecurity, quantum AI, and financial computing-where the proposed model outperforms standard probabilistic reasoning in terms of accuracy, resilience to noise, interpretability, and decision stability. Comparative analysis against QBism, Dempster-Shafer, and fuzzy quantum logic further demonstrates the uniqueness of architecture in both operational semantics and practical outcomes. This contribution lays the groundwork for a new theory of epistemic quantum computing capable of modelling and acting under uncertainty beyond traditional paradigms.
In this work, we propose a novel quantum-informed epistemic framework that extends the classical notion of probability by integrating plausibility, credibility, and possibility as distinct yet complementary measures of uncertainty. This enriched quadruple (P, Pl, Cr, Ps) enables a deeper characterization of quantum systems and decision-making processes under partial, noisy, or ambiguous information. Our formalism generalizes the Born rule within a multi-valued logic structure, linking Positive Operator-Valued Measures (POVMs) with data-driven plausibility estimators, agent-based credibility priors, and fuzzy-theoretic possibility functions. We develop a hybrid classical-quantum inference engine that computes a vectorial aggregation of the quadruples, enhancing robustness and semantic expressivity in contexts where classical probability fails to capture non-Kolmogorovian phenomena such as entanglement, contextuality, or decoherence. The approach is validated through three real-world application domains-quantum cybersecurity, quantum AI, and financial computing-where the proposed model outperforms standard probabilistic reasoning in terms of accuracy, resilience to noise, interpretability, and decision stability. Comparative analysis against QBism, Dempster-Shafer, and fuzzy quantum logic further demonstrates the uniqueness of architecture in both operational semantics and practical outcomes. This contribution lays the groundwork for a new theory of epistemic quantum computing capable of modelling and acting under uncertainty beyond traditional paradigms.
Although new AI systems have been developed based on the integration of information from multiple sources under conditions of uncertainty, classical probabilistic models are unable to provide structured, interpretable, and reliable representations in the presence of contextual and order effects. Specifically, the fundamental principles of Kolmogorov’s assumptions underlying the modeling overlook certain common violations in real-world decision-making processes, such as non-commutativity, contextual dependence among agents, and interaction effects between information sources characterized by experiential heterogeneity. A Positive Operator-Valued Measure (POVM) formalism defined on a Hilbert space of latent states forms the basis of this article’s structured epistemic representation framework to support the reliability and interpretability of the black box in AI. The resulting model generalizes the classical epistemic quadruplet: Probability, Plausibility, Credibility, and Possibility within a single geometric framework in which three essential non-classical effect mechanisms emerge—(i) the non-commutativity of information acquisition, (ii) the contextuality arising from incompatible observational frameworks, and (iii) the interference interactions between information acquisition channels. We propose the concept of a quantum-inspired fusion operator (QI-Happenability), which introduces symmetric and antisymmetric feedback interaction terms based on the estimation of ordered residuals. An analysis of the proposed framework is then performed using real data, validating the model on the Efron et al. diabetes regression dataset (N = 442; ten standardized physiological predictors; continuous disease progression target), available in scikit-learn, which showed a 17.4% reduction in mean absolute error (MAE) compared to traditional models and significant improvements over polynomial machine learning baselines, as well as ensemble machine learning methods, within a rigorous cross-validation protocol. Contextual analysis indicates that 68% of cases violate classical bounds (CHSH inequality, p < 0.001), empirically confirming the non-classical structured representation in multi-source data. The results confirm the proposed approach as a simpler, more interpretable, and more reliable alternative to black-box models: this work demonstrates how the use of structured epistemic representations in reasoning under uncertainty preserves formal interpretability while retaining useful semantic information. By linking quantum cognition and applied AI, this work could help lay the groundwork for a new generation of interpretable and reliable decision-making systems.
Human interaction with the world is dominated by uncertainty. Probability theory is a valuable tool to face such uncertainty. According to the Bayesian definition, probabilities are personal beliefs. Experimental evidence supports the notion that human behavior is highly consistent with Bayesian probabilistic inference in both the sensory and motor and cognitive domain. All the higher-level psychophysical functions of our brain are believed to take the activities of interconnected and distributed networks of neurons in the neocortex as their physiological substrate. Neurons in the neocortex are organized in cortical columns that behave as fuzzy sets. Fuzzy sets theory has embraced uncertainty modeling when membership functions have been reinterpreted as possibility distributions. The terms of Bayes' formula are conceivable as fuzzy sets and Bayes' inference becomes a fuzzy inference. According to the QBism, quantum probabilities are also Bayesian. They are logical constructs rather than physical realities. It derives that the Born rule is nothing but a kind of Quantum Law of Total Probability. Wavefunctions and measurement operators are viewed epistemically. Both of them are similar to fuzzy sets. The new link that is established between fuzzy logic, neuroscience, and quantum mechanics through Bayesian probability could spark new ideas for the development of artificial intelligence and unconventional computing.
Purpose: Decision-making under uncertainty remains a foundational challenge in cognitive science and artificial intelligence. Classical Bayesian Probability Models (CBM) often fail to explain paradoxical cognitive behaviors such as order effects, ambiguity aversion, and context-dependent reasoning. This study seeks to compare Quantum Probability Theory (QPT) and Classical Bayesian Models in their ability to capture the dynamics of human decision-making. It aims to determine which framework more accurately reflects the cognitive mechanisms underlying reasoning under uncertainty. Methodology: A qualitative, exploratory research design was adopted, involving in-depth semi-structured interviews with 16 experts across psychology, philosophy, artificial intelligence, and cognitive neuroscience. Participants were purposively selected for their theoretical and empirical expertise in probabilistic reasoning. Data were analyzed using reflexive thematic analysis, guided by the Dual-Process Theory and Busemeyer’s Quantum Cognition framework. The analysis emphasized participants’ perspectives on theoretical assumptions, cognitive plausibility, and predictive utility between QPT and CBM paradigms. Findings: Thematic findings reveal that Quantum Probability Theory offers superior explanatory power in contexts involving cognitive ambiguity, contextual dependence, and non-commutativity of mental operations. Participants consistently reported that QPT better models real-world reasoning tasks where classical logic collapses, capturing the fluid and context-sensitive nature of human judgment. Conversely, while CBM remains effective in structured, low-uncertainty scenarios, it fails to accommodate superposition and interference effects inherent in human cognition. Unique Contribution to Theory, Practice, and Policy (Recommendations): The study contributes theoretically by demonstrating how quantum probabilistic models expand existing theories of bounded rationality and probabilistic reasoning in cognitive science. Practically, it encourages interdisciplinary collaboration between cognitive scientists, AI researchers, and philosophers to refine decision models that mirror human intuition more closely. Policy-wise, the findings support the integration of quantum-inspired approaches in the design of intelligent decision-support systems and cognitive architectures. The study recommends continued empirical validation of QPT within applied domains—such as behavioral economics, machine learning, and cognitive modeling—to strengthen its predictive and explanatory robustness.
The integration of artificial intelligence (AI) and quantum computing is poised to redefine the landscape of financial risk modeling and enterprise decision-making systems. This paper investigates the synergistic potential of these transformative technologies, emphasizing the development of hybrid AI-quantum algorithms to address the increasing complexity of modern financial systems. Traditional risk modeling methodologies often face significant limitations in capturing intricate market dynamics and accounting for real-time decision-making constraints. By leveraging quantum computing's unparalleled computational capabilities, particularly its ability to handle high-dimensional optimization problems, AI-powered quantum algorithms present a paradigm shift in financial risk prediction and mitigation. The research elaborates on key applications, including portfolio optimization, fraud detection, and credit risk analysis, demonstrating how quantum-enhanced AI algorithms achieve superior performance in terms of accuracy, efficiency, and scalability compared to classical approaches. The study begins by elucidating the theoretical underpinnings of hybrid AI-quantum systems, detailing their algorithmic structures and computational advantages. Quantum-inspired AI techniques, such as quantum neural networks and quantum-enhanced support vector machines, are examined for their ability to process vast datasets with unparalleled speed and precision. Portfolio optimization is analyzed as a case study, showcasing how quantum algorithms excel in minimizing risk while maximizing returns within a multidimensional constraint environment. Similarly, advanced fraud detection systems are explored, where hybrid models significantly improve anomaly detection rates by incorporating quantum-enhanced pattern recognition. The paper also delves into credit risk analysis, emphasizing how AI-quantum solutions can predict default probabilities with unprecedented accuracy, thereby supporting financial institutions in managing systemic risks more effectively. Despite these advancements, the integration of AI and quantum computing into financial ecosystems poses substantial challenges. The research discusses issues such as algorithmic scalability, error mitigation in quantum computations, and the resource-intensive nature of quantum hardware. Furthermore, the implementation of these technologies within the existing fintech landscape is fraught with obstacles, including interoperability with classical systems, regulatory compliance, and the high costs associated with quantum infrastructure. Addressing these challenges requires a multidisciplinary approach, combining expertise in quantum mechanics, AI, and financial engineering to develop robust, scalable solutions. The paper also examines the broader implications of AI-quantum integration for enterprise decision systems. By enabling real-time analysis of volatile markets, these technologies empower organizations to make informed, data-driven decisions, thereby enhancing operational resilience and competitive advantage. Furthermore, the ethical considerations and regulatory frameworks governing the deployment of such advanced systems are critically analyzed, emphasizing the need for transparency, fairness, and accountability in algorithmic decision-making. The findings presented in this study underscore the transformative potential of AI-powered risk modeling in quantum finance. By bridging the gap between theoretical advancements and practical implementations, this research contributes to the growing body of knowledge on hybrid AI-quantum systems and their applications in the financial domain. Ultimately, the integration of AI and quantum computing represents a pivotal development in enterprise decision systems, offering unprecedented opportunities to address the complexities of financial risk management in an increasingly interconnected and uncertain world.
The rapid advancement of artificial intelligence (AI) and quantum computing has introduced new paradigms for solving computationally complex problems beyond the capabilities of classical systems. This paper presents a Quantum Intelligence Platform (QIP), a hybrid quantum-inspired computational framework designed to enhance intelligent decision prediction and optimization in complex environments. The proposed system integrates quantum probabilistic modelling concepts such as superposition and interference with classical machine learning algorithms to improve prediction accuracy and adaptive decision-making. A hybrid architecture combining quantum circuit simulation and classical deep learning modules is developed to enable scalable experimentation without requiring physical quantum hardware. The platform is evaluated on decision prediction and optimization tasks, demonstrating improvements in convergence stability and predictive performance compared to conventional models. Experimental results show that quantum-inspired state representation enhances feature expressiveness and probabilistic reasoning. The proposed framework bridges the gap between theoretical quantum computation and practical intelligent systems, offering a scalable pathway for future quantum-enhanced AI applications.
This paper proposes a comprehensive categorical framework for unifying classical and quantum probabilistic logics. We leverage the inherent compositional and structural advantages of category theory to construct a common mathematical language capable of expressing both Kolmogorovian probability and the non-Boolean structures characteristic of quantum mechanics. By treating systems and processes as objects and morphisms within suitable monoidal categories, we demonstrate how core concepts like states, observables, measurements, and conditioning can be abstractly represented and seamlessly transitioned between classical and quantum domains. The framework utilizes probability monads for classical uncertainty and dagger compact closed categories for quantum processes, showing how these distinct structures can be seen as instances of a more general categorical paradigm. This unification not only provides a deeper foundational understanding of uncertainty across different physical theories but also opens new avenues for developing hybrid probabilistic-logical systems in fields such as artificial intelligence and quantum computation.