Infopaket

Quantum mechanics of particles with spin

ВК 4

Вибіркова дисципліна для ОП

First

2021/2022

6 Semester

3

To know the spin states of the system of particles with spin S=1/2, operators Know the density matrix formalism Know quantum entanglement and signs of entanglement To know the basics of the theory of quantum computing and cryptography, basic quantum algorithms and principles of their operation Know the mathematical apparatus of the theory of quantum measurements To be able to analyze the spin states of a system of particles Be able to find the density matrix of the system, calculate the observables, determine the purity and separability of the state of the system and subsystems To be able to determine the result of measurement of observables in different bases

Full-time form

1. Know the basic laws and concepts from the courses of general physics, statistical physics and quantum mechanics at the basic level. 2. To be able to apply previously acquired knowledge from the courses of mathematical analysis, linear algebra and analytical geometry, mathematical physics, general physics, and quantum mechanics to solve practical problems from the course. 3. To have elementary skills of finding and processing specialized literature, solving algebraic and operator equations.

Мodule 1 Basic formalism. Operators, spin states and density matrix 1. Operators in quantum mechanics 2. Basics of the theory of representations 3. Properties of angular momentum operators 4. Spin and spin functions of a particle with spin s=1/2 5. Operators and spin states of the system of particles with spin s=1/2 6. Pure and mixed quantum states 7. Density matrix of composite systems 8. Entanglement of quantum systems, Schmidt distribution, separability criteria Мodule 2 Elements of the theory of quantum computing. Quantum cryptography 9. Elementary operations on qubits, quantum gates, logical operators 10. Quantum algorithms, parallelism 11. Completeness of quantum mechanics, Bell's inequalities 12. PVM and POVM quantum measurements 13. Quantum teleportation, protocol 14. Quantum cryptography, protocols

1. Доценко І.С., Мальнєв В.М. Вступ до квантової механіки частинок зі спіном. К.: ВИДАВНИЧО-ПОЛІГРАФІЧНИЙ ЦЕНТР “КИЇВСЬКИЙ УНІВЕРСИТЕТ”, 2002. 2. Blum K. Density Matrix Theory and Applications. – Springer, Boston, MA, 1996. 3. Kaye P., Laflamme R., Mosca M. An Introduction to Quantum Computing. – Oxford University Press, N.Y., 2007. 4. Nielsen M., Chuang I. Quantum Computation and Quantum Information. – Cambridge University Press, 2010. 5. McMahon D. Quantum Computing Explained. – Wiley-INTERSCIENCE, 2007. 6. Gilder L. The age of entanglement (When Quantum physics was reborn). – N.Y.: A.A.Knopf, 2008.

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