Selected topics from quantum information theory
- Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava (5 credits)
- subject code 2-FYZ-228, summer semester (2+1h/week)
- prerequisities: quantum mechanics, linear algebra,
- undergraduate and graduate students
- lecturer: Mário Ziman
- Thursdays: 10:00-13:00, RCQI seminar room

Description: We select 2-3 currently interesting research topics depending on the interest of lecturers and students. Potential topics includes quantum communication, quantum entanglement, quantum cryptography, quantum complexity, quantum estimations, quantum thermodynamics, quantum numerical methods, quantum dynamics, quantum measurement, quanutum algorithms, quantum walks, axiomatizations of quantum theory, relativistic quantum information, quantum optics information processing, etc.

Plan for summer 2015 (details will be updated).
§ 1. Shannon information theory (Shannon entropy, min/max entropies)
§ 2. Quantum communication quantities (von Neumann entropy, relative entropy, min/max entropies)
§ 3. Quantum entanglement (LOCC, measures, resource theory)
§ 4. Thermalization (equilibration, emergence of temperature)
§ 5. Work and Heat (thermodynamic entropy, 3rd law)
§ 6. 2nd law
§ 7. Landauer's principle
§ 8. Paradoxes

Exam:
- homeworks (60% of points) + test (40% of points) + (potential oral exam)
- A (>70% points), B(>60%), C(>45%), D(>30% p), E(>20%)

Literature:
- recent research papers, available here http://arxiv.org/archive/quant-ph
- M.Wilde: From Classical to Quantum Shannon Theory (Cambridge 2013), http://arxiv.org/abs/1106.1445
- M.Nielsen, I.Chuang: Quantum Information and Quantum Computation (Cambridge, 2000)
- T.Heinosaari, M.Ziman: The Mathematical Language of Quantum theory (Cambridge, 2012)
- T.Heinosaari, M.Ziman: Guide to mathematical concepts of quantum theory, Acta Physica Slovaca 58, 487-674 (2008)