Applications of quantum statistics inpsychological studies of decision processes

Diederik Aerts, Sven Aerts

Diederik Aerts, Sven Aerts

Alexander Semenovich Holevo

James D. Malley, John S. Hornstein

The three main points of this article are: 1. Quantum mechanical data differ from conventional data: for example, joint distributions usually cannot be defined conventionally; 2. rigorous methods have been developed for analyzing such data; the methods often use quantum-consistent analogs of classical statistical procedures; 3. with these procedures, statisticians, both data-analytic and more theoretically oriented, can become active participants in many new and emerging areas of science and biotechnology. In the physical realm described by quantum mechanics, many conventional statistical and probabilistic assumptions no longer hold. Probabilistic ideas are central to quantum theory but the standard Kolmogorov axioms are not uniformly applicable. Studying such phenomena requires an altered model for sample spaces, for random variables and for inference and decision making. The appropriate decision theory has been in development since the mid-1960s. It is both mathematically and statistically rigorous and conforms to the requirements of the known physical results. This article provides a tour of the structure and current applications of quantum-consistent statistical inference and decision theory. It presents examples, outlines the theory and considers applications and open problems. Certain central concepts of quantum theory are more clearly apprehended in terms of the quantum-consistent statistical decision theory. For example, the Heisenberg uncertainty principle can be obtained as a consequence of the quantum version of the Cramer-Rao inequality. This places concepts of statistical estimation and decision theory, and thus the statistician, at the center of the quantum measurement process. Quantum statistical inference offers considerable scope for participation by the statistical community, in both applications and foundational questions.

Andrei Yu. Khrennikov

Shigenori Tanaka

We review recent theoretical developments linking quantum-like cognition, nonequilibrium thermodynamics, and foundation of quantum mechanics. Empirical studies inpsychology and decision making reveal contextuality, order effects, and violations of classical probability theory that are naturally represented within a Hilbert-space formalism. While quantum-like models clarify how such non-classical structures describe cognitive phenomena, and the Free Energy Principle (FEP) explains why living systems perform variational inference, their conceptual integration has remained incomplete. We here explore a possibility of unifying these concepts in terms of temporally correlated “quantum” states. Reformulating variational free energy as quantum relative entropy, we show that open-system quantum decision models realize a quantum extension of the FEP. Using quantum state-over-time representations, we demonstrate that violations of Leggett–Garg inequalities admit an information-theoretic interpretation as strictly positive lower bounds on a macrorealism-restricted temporal free energy. Extending the framework of thermodynamics of prediction, temporal nonclassicality introduces an additional irreducible energetic cost beyond classical predictive inefficiency. We further examine both material (water–electromagnetic–phonon coherence) and stochastic-network foundations for quantum cognition and decision making, and propose that consciousness may be understood as non-collapsing variational inference sustained by temporally coherent organization in living systems.