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 textbook conceptualization of phenotype creation, "genotype (G) + environment (E) + genotype & environment interactions (GE) phenotype (Ph)", is modeled with open quantum systems theory (OQST) or more generally with adaptive dynamics theory (ADT). The model is quantum-like , i.e., it is not about quantum physical processes in biosystems. Generally such modeling is about applications of the quantum formalism and methodology outside of physics. Macroscopic biosystems, in our case genotypes and phenotypes, are treated as information processors which functioning matches the laws of quantum information theory. Phenotypes are the outputs of the E-adaptation processes described by the quantum master equation, Gorini- Kossakowski-Sudarshan-Lindblad equation (GKSL). Its stationary states correspond to phenotypes. We highlight the class of GKSL dynamics characterized by the camel-like graphs of (von Neumann) entropy: in the process of E-adaptation phenotype's state entropy (disorder) first increases and then falls down - a stable and wellordered phenotype is created. Traits, an organism's phenotypic characteristics, are modeled within the quantum measurement theory, as generally unsharp observables given by positive operator valued measures (POVMs. This paper is also a review on the methods and mathematical apparatus of quantum information biology.

This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable A and B. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables A and B,  so this is AB-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilistic definition, we achieve the Hilbert space characterization of the AB-entangled states as amplitude non-factorisable states. In the tensor product case, AB-entanglement implies standard entanglement, but not vise verse. AB-entanglement for dichotomous observables is equivalent to their correlation, i.e., ⟨AB⟩�≠⟨A⟩�⟨B⟩�. We describe the class of quantum states that are A_uB_u-entangled for a family of unitary operators (u). Finally, observables entanglement is compared with dependence of random variables in classical probability theory.

Our aim is to make a step toward clarification of foundations for the notion of entanglement (both physical and mathematical) by representing it in the conditional probability framework. In Schrodinger's words, this is entanglement of knowledge which can be extracted via conditional measurements. In particular, quantum probabilities are interpreted as conditional ones (as, e.g., by Ballentine). We restrict considerations to perfect conditional correlations (PCC) induced by measurements ('EPR entanglement'). Such entanglement is coupled to the pairs of observables with the projection type state update as the back action of measurement. In this way, we determine a special class of entangled states. One of our aims is to decouple the notion of entanglement from the compound systems. The rigid association of entanglement with the state of a few body systems stimulated its linking with quantum nonlocality ('spooky action at a distance'). However, already by Schrodinger entanglement was presented as knotting of knowledge (about statistics) for one observable A with knowledge about another observable B.

We present a new experiment demonstrating destructive interference in customers' estimates of conditional probabilities of product failure. We take the perspective of a manufacturer of consumer products and consider two situations of cause and effect. Whereas, individually, the effect of the causes is similar, it is observed that when combined, the two causes produce the opposite effect. Such negative interference of two or more product features may be exploited for better modeling of the cognitive processes taking place in customers' minds. Doing so can enhance the likelihood that a manufacturer will be able to design a better product, or a feature within it. Quantum probability has been used to explain some commonly observed "non-classical" effects, such as the disjunction effect, question order effect, violation of the sure-thing principle, and the Machina and Ellsberg paradoxes. In this work, we present results from a survey on the impact of multiple observed symptoms on the drivability of a vehicle. The symptoms are assumed to be conditionally independent. We demonstrate that the response statistics cannot be directly explained using classical probability, but quantum formulation easily models it, as it allows for both positive and negative "interference" between events. Since quantum formalism also accounts for classical probability's predictions, it serves as a richer paradigm for modeling decision making behavior in engineering design and behavioral economics.

Recently, the quantum formalism and methodology have been used in application to the modelling of information processing in biosystems, mainly to the process of decision making and psychological behaviour (but some applications in microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modelling. In this paper, we turn to the famous Schrodinger's book "What is life?" and reformulate his speculations in terms of this theory. Schrodinger pointed to order preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrodinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preserve the order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment E: 1) entropy (disorder) increasing in the process of adaptation to the specific features of E; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.

We present the novel approach to mathematical modeling of information processes in biosystems. It explores the mathematical formalism and methodology of quantum theory, especially quantum measurement theory. This approach is known as quantum-like and it should be distinguished from study of genuine quantum physical processes in biosystems (quantum biophysics, quantum cognition). It is based on quantum information representation of biosystem's state and modeling its dynamics in the framework of theory of open quantum systems. This paper starts with the non-physicist friendly presentation of quantum measurement theory, from the original von Neumann formulation to modern theory of quantum instruments. Then, latter is applied to model combinations of cognitive effects and gene regulation of glucose/lactose metabolism in Escherichia coli bacterium. The most general construction of quantum instruments is based on the scheme of indirect measurement, in that measurement apparatus plays the role of the environment for a biosystem. The biological essence of this scheme is illustrated by quantum formalization of Helmholtz sensation-perception theory. Then we move to open systems dynamics and consider quantum master equation, with concentrating on quantum Markov processes. In this framework, we model functioning of biological functions such as psychological functions and epigenetic mutation.

Differentiation is a universal process found in various phenomena of nature. As seen in the example of cell differentiation, the creation diversity on individual's character is caused by environmental interactions. In this paper, we try to explain its mechanism, which has been discussed mainly in Biology, by using the formalism of quantum physics. Our approach known as quantum bioinformatics shows that the temporal change of statistical state called decoherence fits to describe non-local phenomena like differentiation. (C) 2017 Elsevier Ltd. All rights reserved.

In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory. (C) 2016 Elsevier Inc. All rights reserved.

The authors present the theory of quantum measurements in a humanities friendly way. The most general process of decision-making is represented with the aid of the formalism of quantum apparatuses and instruments. This measurement formalism generalizes the standard one based on the von Neumann–Lüders projection postulate. Generalized quantum observables are mathematically represented as positive operator valued measures (POVMs) and state transformers resulting from the feedback of measurements to the states of systems that are given by quantum instruments. The quantum scheme of indirect measurements (a special realization of quantum instruments) is applied to model decision-making as resulting from the interaction between the belief and decision states. The authors analyze the specific features of quantum instruments which are important for cognitive and social applications. In particular, the state transformers given by quantum instruments are in general less invasive than the state projections. Thus quantum-like decision-making need not be viewed as a kind of state collapse.