Quantum semi-markov system analysis and information processing in a stochastic model with interfering non-target states

Abstract

The article is devoted to the topical issue of dissemination within the framework of quantum semi-Markov system analysis, as one of the possible promising areas of system analysis, of methods of finite semi-Markov processes for the case of complex quantum systems with interfering non-target states. The study of such systems from the standpoint of system analysis means the study, first of all, of the information aspects of the system: goals, signals, information flows. Then semi-Markov processes and states are considered in an extended sense, in which stochasticity is understood in the context of not only probabilities, but also probability amplitudes. A set of interrelated axiological and causal representations of the stochastic model of the dynamics of a complex quantum system is proposed. This dynamics is described in terms of the Feynman formulation of quantum mechanics. Based on the proposed set of representations, it is convenient to carry out quantum semi-Markov system analysis when processing information in the process of modeling the dynamics of the system, as a random in the extended sense process of transitions between a finite number of interfering non-target and incompatible target states according to the specified propagators. This analysis allows us to estimate the attainability of the goal and the timeliness of its achievement by a complex quantum system. The goal of the system is understood here as the achievement of any state belonging to a suitably defined target subset (subspace) of a finite set (space) of all states. The initial data of the analysis are the physical characteristics of the system dynamics in the phase space with the target subspace of physical states of the stochastic model of the system: the initial wave function of the system and its propagators for the specified phase space with the target subspace. The characteristics of the causal representation are expressed through these initial data, and then through them - the axiological one. The causal representation is constructed based on the formalization of the dynamics of a complex quantum system by Markov restoration processes in the extended sense. Such formalization allows us to use the theory of finite semi-Markov processes in the extended sense to construct the characteristics of the axiological representation.