The existing computational cognitive models in cyber security risk management have major limitations in the analysis of cyber security behaviors. To address this issue, we introduce Hilbert space and quantum cognition to cyber security risk management. We compare some key axioms and definitions of classical cognition and quantum cognition. We provide examples on how some unique principles of Hilbert space and quantum cognition such as compatibility can help with the event representation, and capturing cognitive biases that are not possible with classical probability. We shed light on how the mathematical formalism of quantum probability can model the observed deviations from the classicality in human reasoning. We also shed light on how quantum cognition can contribute to the science and practice of cyber security. We argue that Hilbert space and quantum cognition can reconcile violations of classical probability theory in cyber security risk management with a formal theory, and examine whether it is possible to express formally some of the key heuristics in cyber security behaviors.
The existing computational cognitive models in cyber security risk management have major limitations in the analysis of cyber security behaviors. To address this issue, we introduce Hilbert space and quantum cognition to cyber security risk management. We compare some key axioms and definitions of classical cognition and quantum cognition. We provide examples on how some unique principles of Hilbert space and quantum cognition such as compatibility can help with the event representation, and capturing cognitive biases that are not possible with classical probability. We shed light on how the mathematical formalism of quantum probability can model the observed deviations from the classicality in human reasoning. We also shed light on how quantum cognition can contribute to the science and practice of cyber security. We argue that Hilbert space and quantum cognition can reconcile violations of classical probability theory in cyber security risk management with a formal theory, and examine whether it is possible to express formally some of the key heuristics in cyber security behaviors.
Uncertainty is an intrinsic part of life; most events, affairs, and questions are uncertain. A key problem in behavioral sciences is how the mind copes with uncertain information. Quantum probability theory offers a set of principles for inference, which align well with intuition about psychological processes in certain cases: cases when it appears that inference is contextual, the mental state changes as a result of previous judgments, or there is interference between different possibilities. We motivate the use of quantum theory in cognition and its key characteristics. For each of these characteristics, we review relevant quantum cognitive models and empirical support. The scope of quantum cognitive models encompasses fallacies in decision-making (such as the conjunction fallacy or the disjunction effect), question order effects, conceptual combination, evidence accumulation, perception, over-/underdistribution effects in memory, and more. Quantum models often formalize psychological ideas previously expressed in heuristic terms, allow unified explanations of previously disparate findings, and have led to several surprising, novel predictions. We also cast a critical eye on quantum models and consider some of their shortcomings and issues regarding their further development.
The emergence of quantum computing has prompted researchers to examine potential parallels between quantum mechanical principles and human cognitive processes. This article explores the theoretical framework of quantum cognition, examining how concepts from quantum mechanics, including superposition, entanglement, and measurement, might inform our understanding of human decision-making, memory, and consciousness. While quantum computing operates on fundamentally different physical principles than biological neural networks, the mathematical formalisms of quantum mechanics offer novel perspectives on cognitive phenomena that classical probability theory struggles to explain. This review critically examines the current state of quantum cognition research, its applications in computational modeling, and the ongoing debates regarding the validity of quantum mechanical analogies in psychological theory. The analysis reveals both promising theoretical insights and significant limitations in applying quantum principles to human cognition, highlighting the need for empirical validation and careful distinction between mathematical analogy and physical reality.
Contemporary discussions of the gap between natural and artificial intelligence often emphasize human capacities such as contextual reasoning, cognitive flexibility, and non-classical decision-making. This paper proposes that quantum and quantum-like models of cognition and decision processes offer a principled framework for addressing these differences. A growing body of empirical evidence shows that human reasoning systematically violates the assumptions of classical probability and logic, exhibiting contextuality, order effects, interference phenomena, and task incompatibility. Quantum probability theory and related quantum-like formalisms provide mathematically rigorous tools—based on Hilbert spaces, superposition, and entanglement—that capture these features more naturally than classical models. While quantum and quantum-like approaches share a common mathematical structure, they differ in physical implementation, motivating two complementary directions in artificial intelligence: quantum AI and quantum-like AI. Together, these approaches suggest a viable pathway toward narrowing, and potentially bridging, the divide between natural and artificial intelligence by grounding AI architectures in models aligned with the structure of human cognition.
The purpose of this article is to discuss principle ideas of quantum cognition research program, which comprise elements of the formalism of quantum mechanics (mainly Hilbert space theory and quantum probability theory) for modeling human cognition and decision processes. In the opinion of authors of this program, paradox empirical findings in psychological literature may be explained based on concepts of quantum mechanics. Formally, there is described a discrete-time random chain χ which is defined on a finite interval [0, T] and χ(t) can assume only finite number of values. The space H of such processes will be finite-dimensioned. Then some properties and applications of the quantum probability space on H are studied.
Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality.
Classical models of decision-making under uncertainty, grounded in expected utility theory and Bayesian probability, often fail to account for systematic cognitive anomalies such as preference reversals, order effects, ambiguity aversion, and context-dependent choices. Quantum cognition models offer a novel theoretical framework that applies the mathematical principles of quantum probability—such as superposition, interference, and non-commutativity—to cognitive processes without assuming physical quantum mechanisms in the brain. By representing cognitive states as probabilistic superpositions that collapse through decision “measurements,” these models provide parsimonious explanations for violations of classical rationality. This paper examines how quantum cognition frameworks capture contextual influence, belief updating, and interference effects in uncertain decision environments. Drawing on findings from cognitive psychology and behavioral economics, the study highlights the relevance of quantum cognition for applications in economic choice modeling, legal decision analysis, and artificial intelligence. The analysis suggests that quantum probability offers a robust alternative to classical approaches when modeling human decision-making in complex, ambiguous, and context-sensitive situations.