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Acta Polytechnica

Wave Probabilistic Model of Binary Time Series

Miroslav Svítek

Published Jan 5, 2008• 1 citation
Publisher

Abstract

This paper presents the theory of wave probabilistic models, together with important features, such as the inclusion-exclusion rule, the product rule, the complementary principle and entanglement. These features are mathematically described, and an illustrative example of binary time series is shown to demonstrate possible applications of the theory.

DOI
10.14311/1055

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This paper presents the theory of wave probabilistic models, together with important features, such as the inclusion-exclusion rule, the product rule, the complementary principle and entanglement. These features are mathematically described, and an illustrative example of binary time series is shown to demonstrate possible applications of the theory.
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The paper presents the theory of wave probabilistic models together with their features that represent basic principles of quantum informatics. These features are mathematically described and the illustrative examples are shown to demonstrate the possible applications of the presented theory. The proposed methodology represents the original approach which comes from defined mathematical assumptions like single-valuedness, resonance principle, etc. From these simple assumptions a lot of principle of quantum informatics can be derived like quantization principle, spin, entanglement, etc.
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We have seen that there is an intimate relationship between probability and information. The values we assign to probabilities depend on the information available, and information is a function of probabilities. This connection makes it inevitable that information will be an important concept in any statistical theory, including thermodynamics and, of course, quantum physics. The probabilistic interpretation of quantum theory has probability amplitudes rather than probabilities as the fundamental quantities. This feature, together with the associated superposition principle, is responsible for intrinsically quantum phenomena and gives quantum information theory its distinctive flavour. We shall see that the quantum rules for dynamical evolution and measurement, together with the existence of entangled states, have important implications for quantum information. They also make it possible to perform tasks which are either impractical or impossible within the classical domain. In describing these we shall make extensive use of simple but fundamental ideas in quantum theory. This chapter introduces the mathematical description of quantum physics and the concepts which will be employed in our study of quantum information.