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IEEE International Conference on Soft Computing and Measurements (SCM)

The space-time formalism in description of quantum information object characteristic properties in the context of problem-solving of observable quantities soft measurements for CARD-systems VI-environments

И. В. Герасимов, Sergey A. Kuzmin, N. M. Safiannikov

Published May 1, 2015• 2 citations
Publisher

Abstract

The purpose of this report is the presentation of an original approach for complementary modeling of quantum information objects (quantum circuits) in the virtual instruments environments (VI-environments). While doing the research work the algebraic-topological apparatus for identifying fractal-time structure of the observed signal based on physical phenomenology and p-adic metrics was used. The main result of the work is a new cognitive strategy of multidimensional methodological thinking, based on the following principles: modeling, diversification, complementarity, virtualization, tolerance, duality. The conclusions emphasize the relationship between asynchronous VI-environments ideology and Bergson's philosophy: the events produced by VI-environment components interaction, are objectively exist - they appear and disappear, simulating, thus, some continuous time flow.

DOI
10.1109/scm.2015.7190471

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The purpose of this report is the presentation of an original approach for complementary modeling of quantum information objects (quantum circuits) in the virtual instruments environments (VI-environments). While doing the research work the algebraic-topological apparatus for identifying fractal-time structure of the observed signal based on physical phenomenology and p-adic metrics was used. The main result of the work is a new cognitive strategy of multidimensional methodological thinking, based on the following principles: modeling, diversification, complementarity, virtualization, tolerance, duality. The conclusions emphasize the relationship between asynchronous VI-environments ideology and Bergson's philosophy: the events produced by VI-environment components interaction, are objectively exist - they appear and disappear, simulating, thus, some continuous time flow.
We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so called transformers of information, basic processes are information processes, the statistics are information statistics (thus we present a model of information reality). The classical and quantum mechanical formalisms on information p-adic spaces are developed. It seems that classical and quantum mechanical models on p-adic information spaces can be applied for the investigation of flows of information in cognitive and social systems, since a p-adic metric gives quite natural description of the ability to form associations.
Based on classical mechanical picture of physical objects, quantum-mechanical measurements are formulated and analyzed in an abstract way. We interpret a dynamical flow generated by a Hamiltonian vector field as a description of the effect on the objects caused by a device or an environment. By expressing contexts of measurement explicitly, a matrix representation of observables on a finite dimensional Hilbert space is constructed. A quantum-mechanical state vector is introduced as something on which a dynamical flow generated by a Hamiltonian vector field acts. We find conditions that enable us to obtain the Dirac's quantization rule for the mean values. At the same time, several characteristics (i.e., rectifiability, a generator of symmetry, an invariant mean) of quantum-mechanical measurements are formulated in our formalism.
The rapid development of the chemical industry and science and new challenges in the field of health care put forward increased demands for the development of the theory of organic and inorganic chemistry, biochemistry and biophysics, the search and implementation of new modelling and analysis methods, and the improvement of technological processes. One of the safe and fast methods of researching the properties and behavior of new materials and tools is the modelling of relevant experiments, in particular, computer molecular modelling based on mathematical models. Modelling the interactions between micro and macromolecules at the quantum level allows us to manipulate the substances’ electronic, magnetic, optical and other characteristics and consider the possibilities of creating new chemical bonds, molecular structures, phase transitions, quantum states, and so on. Accordingly, the main idea of our research is to apply the technology of algebraic modelling and quantum-chemical apparatus for the simulation and verification of experiments in physics, chemistry, and biology areas. The use of formal algebraic methods allows proving properties and finding relevant scenarios for the effective analysis of the behavior of various objects in real-time, considering not individual scenarios but sets of possible behaviors. At this research stage, we have developed a methodology for formalization complex organic and inorganic substances, chemical processes and reactions based on the formalization of the interaction of atoms and molecules at the level of quantum interactions.
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.
We describe spacelike and timelike (causally connected) events on an equal footing by utilizing detectors coupled to timers that store information about a given system and the moment of measurement. By tracing out the system and focusing on the detectors' and timers' states, events are represented by a tensor product structure. Furthermore, including a time register gives rise to a temporal superposition analogous to the familiar spatial superposition in quantum mechanics. We verify that the presence of coherence can ensure a causal connection between events. We also propose a causal correlation function involving the detection times to characterize the type of events. Finally, we verify that our formalism allows us to simultaneously apply quantum information concepts to spacelike and timelike events. In this context we observe, in the limit of instantaneous measurements, a deterministic relationship between causally connected events similar to that of spatially entangled physical systems; i.e. observing the state of one of the systems (in our case, knowing a previous event), enables us to learn precisely the state of the other system (we delineate a later event).
Schrödinger's cat states A prerequisite to getting quantitative information on the microscopic world is the existence of measuring apparatuses that indicate definite measuring results.The idea that a pointer of a measuring device is itself in an indeterminate state waiting for someone to make the wavefunction for the combined system (object + measuring apparatus) collapse by simply having a look on the apparatus, thus reading it out, appears absurd. I think, there is no doubt that measuring devices will behave like other objects in the macroscopic world in which there is no place for ‘intrinsic’ uncertainty. Actually, this fact becomes questionable, at least it needs further theoretical investigation, when it is claimed that the quantum mechanical description applies also to macroscopic bodies, in particular measuring devices. (There are physicists who do not shrink back from attributing a single wavefunction even to the whole universe!) The dilemma originates from the quantum mechanical rule following from the linearity of the Schrödinger equation, that a pure quantum state remains a pure quantum state during its evolution. So, assuming that both the microscopic system to be observed and the measuring apparatus are initially in a pure state each, the combined system (object + measuring apparatus) will still be in a pure state after the interaction has taken place. Hence one will need ‘someone’ to bring about the collapse of the wavefunction. (In a realistic approach to this problem, the agent is recognized to be the environment with its virtually infinite number of degrees of freedom.) Schrödinger, being fully aware of this dilemma, illustrated it ingeniously through a fictitious ‘diabolic device’.