## 1 Introduction  
Recent years have been characterized by tremendous development of quantum information theory and engineering. We note that from the quantum information viewpoint, it is not surprising that the quantum formalism can be used to model behavior of cognitive systems (see Reference [1, 2]). And we can point to the wave of interest to quantum-like models in cognition, psychology, and decision-making. The main stimulus for development of quantum-like modeling came from decision theory that has been suffering of numerous paradoxes, some of them unresolvable by means of the traditional methods. We point out that [PERSON] and [PERSON] [3, 4] and other researchers in psychology and economics (starting with the seminal paradoxes of [PERSON] [5] and [PERSON] [6]) demonstrated cases where _classical probability_ (CP) prescription and actual human thinking persistently diverge, at least relative to baseline classical intuitions. There is a plenty of probabilistic data that does not match the laws of CP. These data were typically related to probability fallacies and irrational behavior. [PERSON] and [PERSON] advertised the heuristic approach as an alternative to CP-modeling. However, it was shown that some of the main problems of the CP-based decision-making can be resolved on the basis of _quantum probability_ (QP) calculus. The QP-approach to modeling of decision-making is a purely operational approach describing probability distributions of observations'outputs. The quantum formalism is used to describe aforementioned data, to resolve paradoxes, and to model various psychological effects, such as conjunction, disjunction, and order effects; see, e.g., monographs [1,2,7,8,9,10] and some representative papers [11,12,13,14,15,16,17]. The main tool is the machinery of quantum interference for incompatible observables [1,8]; see also [2,18] for tests of contextuality in decision-making based on the Bell-type [19] inequalities. In many cases, models based on quantum theory can be seen as providing a formalization of relevant heuristic principles (e.g., the quantum model for the _conjunction fallacy_[12] can be thought of as a formalization of [PERSON] and [PERSON]'s _representativeness heuristic_[4]). As is often the case with cognitive models [20], in the quantum-like approach, the brain is considered as _a black box_ that processes information in accordance with the laws of quantum information theory and generates QP-data. The quantum-like community is multi-disciplinary, with around two hundred experts (approximately 5500 links at Google scholar). The main problem of quantum-like modeling is its shaky neurophysiological ground. Although the black box model has found numerous applications, one can be curious in coupling between the quantum information model of processing of mental information by the brain and neurophysiological processes in the brain. The first steps in this direction were done in Reference [21, 22, 23]. We now briefly describe the basis components of the quantum-like model coupling electrochemical process in the brain with quantum information process of information:  
* 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 (Section 2). * The brain's psychological functions perform self-measurements by extracting from quantum information states concrete answers to questions, or solutions of problems (Section 4). * This extraction is modeled in the framework of theory of _open quantum systems_ (Section 6). (In this way, it is possible to proceed without appealing to the state's collapse. The latter is the most mystical postulate of quantum theory (see Section 5). Thus, we do not want to use it.) * Dynamics of the (quantum information) state of psychological function \(F\) is described by the quantum master equation (Section 6). Its stationary states represent classical statistical mixtures of possible outputs of \(F\) (decisions).