IA082 Selected themes of quantum mechanics

Faculty of Informatics
Autumn 2018
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. Mgr. Mário Ziman, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Wed 18:00–19:50 B411
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After this course students should:
understand basic principles of quantum physics;
apply the learned concepts in the subsequent study of quantum information theory;
self-study quantum theory books.
Syllabus
  • 1. Security and computation with photons - photon's polarization and polarizers, Vernam cipher, quantum key "distribution" protocol B92, polarizing beam-splitter, √NOT logic gate,
  • 2. Quantum interference and superposition - Mach-Zender interferometer, concept of quantum state, quantum probabilities and amplitudes, Hilbert space and operators,
  • 3. Measuring quantum properties - description of quantum measurement devices (POVM), tomography of polarization, uncertainty relations, no information without disturbance
  • 4. Hydrogen atom - emission spectrum, Bohr's model, position and momentum, quantum solution, Zeeman effects, spin of electron,
  • 5. Schrodinger equation - time and evolution, unitary operators, energy conservation and system's Hamiltonian,
  • 6. Quantum bit - two-level quantum system (polarization and spin-1/2), Stern-Gerlach experiments, Bloch sphere, orthogonality and information, no-cloning theorem, quantum NOT gate, qubit implementations
  • 7. Quantum sources and randomness - mixed states, quantum commpression, von Neumann entropy, capacity of noiseless quantum channel, randomness sources, min-entropy
  • 8. Einstein-Podolski-Rosen paradox - composite quantum systems, tensor product, quantum steering, EPR paradox, local hidden variable model, CHSH inequalities, experiments and loopholes
  • 9. Quantum one-time pad protocols - one-time pad, super-dense coding and teleportation
  • 10. Quantum entanglement - correlated and separable states, definition of entanglement, entanglement distilation,
  • 11. Quantum cryptography - QKD protocols BB84, E91, no-quantum bit commitment theorem, quantum secret sharing protocols,
  • 12. Elementary particles - fermions and bosons and tensor products, standard model, Higg's boson
Literature
  • ZIMAN, Mário. Vybrané kapitoly z kvantové mechaniky (Selected topics from quantum mechanics). 2004. URL info
Teaching methods
Lectures
Assessment methods
Homeworks and written exam, usage of materials and notes is allowed, optional oral exam
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://quantum.physics.sk/rcqi/index.php?x=fimu_qm
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Autumn 2018, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2018/IA082