MicroCloud Hologram Develops Multi-Domain Quantum Probability Model
MicroCloud Hologram Inc., is a technology service provider. In important fields such as quantum measurement theory, quantum information processing, quantum computing, quantum decision theory (QDT), and artificial quantum intelligence, a universal and mathematically rigorous definition of quantum probability has become a critical need. Since the birth of quantum theory, the definition of quantum probability for operational measurable events has been widely known and applied, but its definition for composite events (corresponding to non-commutative observables) has remained an unresolved challenge. This issue becomes particularly prominent when quantum methods are applied to psychological and cognitive sciences, as these fields involve not only operational testable events but also a large number of decision-making processes corresponding to uncertain events. In real life, decision-making under uncertainty is not an exception but a typical and prevalent situation, making the problem of defining quantum probability for composite events even more valuable for research. When applying quantum theory to psychology and cognitive sciences, researchers often tend to construct specialized models for specific decision-making cases. However, HOLO believes that quantum decision theory must be developed into a universal theory applicable to any situation and must share the same mathematical foundation as quantum measurement theory.
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In fact, quantum measurement theory can essentially be interpreted as a form of decision theory: there is a direct correspondence between the measurement process and the decision-making process—measurements correspond to events, operationally testable measurements correspond to definite events, undefined measurements correspond to uncertain events, and composite measurements correspond to composite decisions. This correspondence can be established with only slight adjustments in expression, providing a logical basis for constructing a unified theory.
The universal theory proposed by HOLO takes the precise definition of quantum probability as its core, with a clear and unique mathematical foundation, applicable simultaneously to both quantum measurement and quantum decision-making scenarios. The key to this definition lies in covering all types of measurements and events: whether they are operationally testable definite events or non-deterministic events, basic events or composite events, corresponding to commutative observables or non-commutative observables, all can be described with a consistent and rigorous probability framework. This characteristic breaks through the limitations of traditional quantum probability definitions, enabling the theory to handle complex composite events, especially those involving non-commutative observables, and providing a new tool for explaining uncertain decision-making in psychological and cognitive sciences.
This universal theory must meet multiple applicability requirements: at the system level, it must be adaptable to both closed systems (such as independent decision-making by isolated individuals) and open systems (such as information interactions in group decision-making); at the decision-making entity level, it must be applicable simultaneously to individual decision-makers and social group decision-makers. The universality of the theory is also reflected in its inclusivity of classical theories—incorporating classical decision theory as a special case, where quantum probability automatically reduces to classical probability when all observables are commutative. Furthermore, the theory must clearly define the applicable boundaries of quantum technology: when events exhibit strict commutativity and uncertainty can be fully quantified, classical methods are sufficient; when non-commutative observables or vague uncertainties are involved, the quantum framework must be employed.
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Unlike descriptive modeling, HOLO emphasizes quantitative predictive capabilities, achieving numerical simulations of decision outcomes by establishing evolutionary equations for decision states and mathematical mappings of observables. For example, in risk decision experiments, choice probabilities calculated based on quantum probability can precisely fit actual behavioral data, with errors significantly lower than those of classical utility models; in the analysis of group opinion evolution, the theory can quantitatively predict critical points and trends in opinion shifts. This quantitative predictive capability enables the theory not only to explain paradoxes that classical theories cannot address but also to provide verifiable scientific evidence for practical applications such as psychological interventions and policy formulation. As the theory matures, its application scope is expected to expand from psychological experiments to fields such as economic forecasting and social governance, promoting the deep application of quantum methods in complex system research.
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