Toeplitz Determinants, Fisher-Hartwig Formula and Entropy

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The project develops a new powerful method of evaluation of entanglement in various dynamical systems. The method uses Toeplitz determinants and the Fisher-Hartwig formula. Entanglement is a primary resource in quantum information processing, necessary for quantum computation and communication. The idea of the project is to find a physical system with maximum entanglement available to control. The entropy of a subsystem is used in the project as a measure of entanglement; it defines the dimension of the Hilbert space of the subsystem.Development of high-performance computing is a strategically important goal. A promising approach to the construction of fast computers is based on quantum mechanics. In order to build quantum computers, and it is necessary to identify physical systems with a large degree of inherently quantum-mechanical behavior. A qualitative measure of such 'quantumness' is entanglement. This project develops a method for searching for physical systems with maximal entanglement.