In this work, we conduct a sentiment analysis of English-language reviews using a quantum-like (wave-based) model of text representation. This model is explored as an alternative to machine learning (ML) techniques for text classification and analysis tasks. Special attention is given to the problem of segmenting text into semantic units, and we illustrate how the choice of segmentation algorithm is influenced by the structure of the language. We investigate the impact of quantum-like semantic interference on classification accuracy and compare the results with those obtained using classical probabilistic methods. Our findings show that accounting for interference effects improves accuracy by approximately 15%. We also explore methods for reducing the computational cost of algorithms based on the wave model of text representation. The results demonstrate that the quantum-like model can serve as a viable alternative or complement to traditional ML approaches. The model achieves classification precision and recall scores of around 0.8. Furthermore, the classification algorithm is readily amenable to optimization: the proposed procedure reduces the estimated computational complexity from O(n2) to O(n).

Quantum-like (QL) modeling, one of the outcomes of the quantum information revolution, extends quantum theory methods beyond physics to decision theory and cognitive psychology. While effective in explaining paradoxes in decision making and effects in cognitive psychology, such as conjunction, disjunction, order, and response replicability, it lacks a direct link to neural information processing in the brain. This study bridges neurophysiology, neuropsychology, and cognitive psychology, exploring how oscillatory neuronal networks give rise to QL behaviors. Inspired by the computational power of neuronal oscillations and quantum-inspired computation (QIC), we propose a quantum-theoretical framework for coupling of cognition/decision making and neural oscillations-QL oscillatory cognition. This is a step, may be very small, toward clarification of the relation between mind and matter and the nature of perception and cognition. We formulate four conjectures within QL oscillatory cognition and in principle they can be checked experimentally. But such experimental tests need further theoretical and experimental elaboration. One of the conjectures (Conjecture 4) is on resolution of the binding problem by exploring QL states entanglement generated by the oscillations in a few neuronal networks. Our findings suggest that fundamental cognitive processes align with quantum principles, implying that humanoid AI should process information using quantum-theoretic laws. Quantum-Like AI (QLAI) can be efficiently realized via oscillatory networks performing QIC.

The past few years have seen a surge in the application of quantum-like (QL) modeling in fields such as cognition, psychology, and decision-making. Despite the success of this approach in explaining various psychological phenomena, there remains a potential dissatisfaction due to its lack of clear connection to neurophysiological processes in the brain. Currently, it remains a phenomenological approach. In this paper, we develop a QL representation of networks of communicating neurons. This representation is not based on standard quantum theory but on generalized probability theory (GPT), with a focus on the operational measurement framework (see section 2.1 for comparison of classical, quantum, and generalized probability theories). Specifically, we use a version of GPT that relies on ordered linear state spaces rather than the traditional complex Hilbert spaces. A network of communicating neurons is modeled as a weighted directed graph, which is encoded by its weight matrix. The state space of these weight matrices is embedded within the GPT framework, incorporating effect-observables and state updates within the theory of measurement instruments - a critical aspect of this model. Under the specific assumption regarding neuronal connectivity, the compound system S = (S₁, S₂) of neuronal networks is represented using the tensor product. This S₁ ⊗ S₂ representation significantly enhances the computational power of S. The GPT-based approach successfully replicates key QL effects, such as order, non-repeatability, and disjunction effects - phenomena often associated with decision interference. Additionally, this framework enables QL modeling in medical diagnostics for neurological conditions like depression and epilepsy. While the focus of this paper is primarily on cognition and neuronal networks, the proposed formalism and methodology can be directly applied to a broad range of biological and social networks. Furthermore, it supports the claims of superiority made by quantum-inspired computing and can serve as the foundation for developing QL-based AI systems, specifically utilizing the QL representation of oscillator networks.

We study the dynamics of von Neumann entropy driven by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation, focusing on its camel-like behavior - a hump-like entropy evolution reflecting the system's adaptation to its environment. Within this framework, we analyze quantum correlations under decoherence and environmental interaction for three sets of quantum states. Our results show that the sign of the entanglement entropy's derivative serves as an indicator of the system's drift toward either classical or quantum information exchange-an insight relevant to quantum error correction and dissipation in quantum thermal machines. We parameterize quantum states using both single-parameter and Bloch-sphere representations, where the angle theta on the Bloch sphere corresponds to the state's position. On this sphere, we construct gradient and basin maps that partition the dynamics of quantum states into stable and unstable regions under decoherence. Notably, we identify a Braiding ring of decoherence-unstable states located at theta=3 pi 4; these states act as attractors under a constructed Lyapunov function, illustrating the topological and dynamical complexity of quantum evolution. Finally, we propose a testable experimental setup based on camel-like entropy and discuss its connection to the theoretical framework of this entropy behavior.

We propose a quantum-inspired framework for modeling open distributed intelligence systems (DISs) comprising natural intelligence agents (NIAs) and artificial intelligence agents (AIAs) that interact with each other. Each NIA - AIA pair represents a user and their digital assistant - an avatar implemented as an agent based on a large language model (LLM). The AIAs are interconnected through a complex, scale-free network and communicate with users and one another in real time. We focus on the social impact and evolution of users' emotional states, which we model as simple, two-level cognitive systems shaped by interactions with AIAs and external information sources. Within this framework, the AIAs adiabatically follow the NIAs, mediating emotional influence by disseminating information and propagating user emotions throughout the system. Building on Mehrabian's Pleasure-Arousal-Dominance (PAD) model and Wundt's three-dimensional theory of emotions, we put forward a quantum-like representation of affective states on an emotional sphere. We demonstrate that the arousal component is governed by the interplay between external informational inputs and individual personality traits. This leads to the emergence of limiting cycles in emotional dynamics. Assuming weak AIA - AIA coupling, we identify two distinct regimes of affective behavior. In the first regime, coherent NIA - AIA interaction supports emotional heterogeneity and individual differentiation across the network. In the second regime, shared exposure to external information drives synchronized emotional responses, resulting in a macroscopic affective field that captures collective emotional dynamics. Furthermore, we demonstrate that the network's structural properties, particularly node degree correlations, play a role analogous to quantum correlations in ensembles of two-level physical systems; a quantum-like superradiant state corresponds to the network-induced collective emotional activation of NIAs within a DIS. These findings advance our understanding of affective dynamics and emergent social phenomena in hybrid human-AI ecosystems.

We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision-making)-quantum-like modelling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects (RREs), cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely, sharp repeatable non-projective measurements-SRP. This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modelling is not the automatic borrowing of the quantum formalism. Exploring the class SRP highlights the role of non-commutativity of the state-update maps generated by measurement back action. Thus, 'non-classicality' in quantum physics as well as quantum-like modelling for cognition is based on two different types of non-commutativity, of operators (observables) and instruments (state-update maps): observable non-commutativity versus state-update-non-commutativity. We speculate that distinguishing quantum-like properties of the cognitive effects is the expression of the latter, or possibly both.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.

Quantum-like modeling (QLM)-quantum theory applications outside of physics-are intensively developed with applications in biology, cognition, psychology, and decision-making. For cognition, QLM should be distinguished from quantum reductionist models in the spirit of Hameroff and Penrose, as well as Umezawa and Vitiello. QLM is not only concerned with just quantum physical processes in the brain but also with QL information processing by macroscopic neuronal structures. Although QLM of cognition and decision-making has seen some success, it suffers from a knowledge gap that exists between oscillatory neuronal network functioning in the brain and QL behavioral patterns. Recently, steps toward closing this gap have been taken using the generalized probability theory and prequantum classical statistical field theory (PCSFT)-a random field model beyond the complex Hilbert space formalism. PCSFT is used to move from the classical "oscillatory cognition" of the neuronal networks to QLM for decision-making. In this study, we addressed the most difficult problem within this construction: QLM for entanglement generation by classical networks, that is, "mental entanglement." We started with the observational approach to entanglement based on operator algebras describing "local observables" and bringing into being the tensor product structure in the space of QL states. Moreover, we applied the standard states entanglement approach: entanglement generation by spatially separated networks in the brain. Finally, we discussed possible future experiments on "mental entanglement" detection using the EEG/MEG technique.

In the framework of relational information, we explore analogs of physical theories and their properties. Specifically, we investigate the causal characteristics of relational information, examining how initial knowledge impacts future relational understanding of the universe/system. To achieve this, we establish a parameter space defining relational structures called dendrograms, exhibiting causal properties akin to those of Minkowski metric. Subsequently, we propose a statistical-dynamical model on this Minkowski-like parameter space, unifying Bohmian and Many Worlds interpretations of quantum theory in the framework of relational information. Additionally, we provide an analytical proof of the non-ergodicity of the relational information framework, revealing CHSH inequality violations as an emergent phenomenon. Our focus on relational information underscores its significance across scientific disciplines, where a single measurement or observation lacks meaning without context.