Psychological information processing in a complex Hilbert space

Andrei Yu. Khrennikov, Masanari Asano

We present the quantum-like model of information processing by the brain’s neural networks. The model does not refer to genuine quantum processes in the brain. In this model, uncertainty generated by the action potential of a neuron is represented as quantum-like superposition of the basic mental states corresponding to a neural code. Neuron’s state space is described as complex Hilbert space (quantum information representation). The brain’s psychological functions perform self-measurements by extracting concrete answers to questions (solutions of problems) from quantum information states. This extraction is modeled in the framework of open quantum systems theory. In this way, it is possible to proceed without appealing to the state’s collapse. Dynamics of the state of psychological function F is described by the quantum master equation. Its stationary states represent classical statistical mixtures of possible outputs of F (decisions). This model can be used for justification of quantum-like modeling cognition and decision-making. The latter is supported by plenty of statistical data collected in cognitive psychology.

Diederik Aerts, Lyneth Beltran, Massimiliano Sassoli de Bianchi +2 more

Jochen Rau

Andrei Yu. Khrennikov

We consider transition from the classical statistical model to the quantum statistical model through ignorance (of huge volume) of information in process of construction of a wave function { a complex probability amplitude. Our approach clarifles relation between classical and quantum statistical models (and hence relation between classical and quantum information theories). In particular, it can be considered as a step toward demystiflcation of quantum theory. The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities.In our approach it is forbidden to consider abstract context independent probabilities: \flrst context and then probability. In this way we obtain interference of probabilities without to appeal to the Hilbert space formalism or wave mechanics. Our formalism can be applied to various domains outside quantum physics, e.g., cognitive sci- ences, psychology, economics, chemistry: roughly speaking in any domain in that it is impossible to extract the whole information about an ontic (or to say realistic) model and hence the epis- temological (experimental or to say observational) model is constructed through huge reduction of information volume. We introduced a notion of prespace { space of states containing complete information about systems under consideration. Classical phase space and quantum Hilbert space are obtained as projections of such a prespace.

Bahaa E. A. Saleh

M. Canan

Two people in the same situation may ascribe very different meanings to their experiences. They will form different awareness, reacting differently to shared information. Various factors can give rise to this behavior. These factors include, but are not limited to, prior knowledge, training, biases, cultural factors, social factors, team vs. individual context, time, resources, and technology. At the individual level, the differences in attaining separate actions by accessing shared information may not be considered as an anomaly from the perspective of rational decision-making. But for group behavior, reacting differently to the shared information can give rise to conflicts and deviations from an expected behavior, and are categorized as an anomaly or irrational behavior. The lack of proper recognition of the reasons for differences can even impede the shared action towards attaining a common objective. The manifestation of differences becomes noticeable in complex situations. The shared awareness approaches that originate from available situational awareness models fail to recognize the reasons of an unexpected decision in these situations. One reason for this is that in complex situations, incompatible events can become dominant. Human information processing is sensitive to the compatibility of the events. This, and various other human psychological characteristics, require models to be developed that include comprehensive formalisms for both compatible and incompatible events in complex situations. Quantum probability provides a geometrical probabilistic formalism to study the decision and the dynamic cognitive systems in complex situations. The event representation in Hilbert space provides the necessary foundation to represent an individual's knowledge of a situation. Hilbert space allows representing awareness as a superposition of indefinite states. These states form a complete N-dimensional Hilbert space. Within the space generated, events are represented as a subspace. By using these characteristics of Hilbert space and quantum geometrical probabilities, this study introduces a representation of self and other-than-self in a situation. An area of awareness with the possibility of projection onto the same event allows representing shared awareness geometrically. This formalism provides a coherent explanation of shared awareness for both compatible and incompatible events. Also, by using the superposition principles, the dissertation introduces spooky action at a distance concept in studying shared awareness.