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Operator algebras and quantum information theory

Вибіркова дисципліна для ОП

Second

2021/2022

3 Semester

8

PLO21.3. Understand the fundamental areas of mathematics and computer science, to the extent necessary for learning mathematical disciplines, applied disciplines and using their methods in a chosen profession. PLO22.3. Understand the main areas of mathematical logic, theory of algorithms and computational theory, programming theory, probability theory and mathematical statistics. PLO23.3. Be able to use professional knowledge, skills and abilities in the field of fundamental sections of mathematics and computer science for research of real processes of different nature. PLO24.3. Be able to independently analyze the relevant subject area, be able to develop mathematical and structural algorithmic models.

To successfully learn the discipline the student should satisfy the following requirements. They know (a) classical courses “Calculus”, “Linear algebra”, “Functional Analysis”, “Probability theory” They can (a) analyze the nature and goals of construction of mathematical structures and models; (b) apply classical commutative methods and construct their non-commutative analogs for solving of actual problems of operator theory and information theory. They should be able to (a) apply classical methods of Linear Algebra, Calculus and Functional Analysis, Probability Theory (b) seek information in open sources and properly analyze it.

The discipline of the second block is aimed at learning basic results of the Operator Algebras theory and mastering technical tools for applications in related areas of applied mathematics. The subject matters includes classical theorems of spectral theory, commutative Banach and C*-algebras, realisation of abstract C*-algebras by Hilbert space operators, structure theorems for the families of orthogonal projections. Applications of the results mentioned above in quantum information theory. The presented course is a natural continuation of the disciplines “Linear Algebra” and “Functional Analysis”.

1. Wegge-Olsen N.E. K-Theory and C*-algebras: a friendly approach. New-York: Oxford Science Publications. The Clarendon Press, Oxford University Press, 1993. – 370 p. 2. Hille E., Phillips R.S. Functional analysis and semigroups. Providence: AMS, 1974.—808 p. 3. Conway J.W.. A Course in Functional Analysis. Second edition. Graduate Texts in Mathematics, 96. New York: Springer-Verlag,1990. – 399 p. 4. S.M. Barnett, Quantum information theory. Oxford University Press, 2009, 300 p.

Lectures, consultations, test works, independent work.

Intermediate assessment: The maximal number of available points is 60. Test work no. 1: 30/18 points. Test work no. 2: 30/18 points. Final assessment (in the form of exam): The maximal number of available points is 40. The form of exam: writing. The types of assignments are 4 writing assignments (2 theoretical and 2 practical).

Ukrainian