Selected chapters from quantum mechanics

- Faculty of Informatics, Masaryk University, Brno
- code: IA082
- B411, Wednesdays 18:00-19:30
- winter semester
- lecturer: Mario Ziman

Descpription: These lectures are meant to be for students of informatics illustrating the basics of quantum physics on quantum information theory examples and applications, mainly in the area of quantum communication and cryptography. It is really helpful if students have elementary background in vector spaces, linear algebra and mathematical analysis. Looking for a bachelor, or master research topic in this field? Do not hesitate to contact me at ziman@savba.sk.

Plan:

§ 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
- double-slit experiment, 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. Schr\"odinger 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,

Recommended literature:
• Mário Ziman: Incomplete lecture notes pdf súbor (in Slovak)
• Vladimír Bužek: Lecture notes link (in Slovak)
• J.Pišút, I.Gomolčák, V.Černý: Úvod do kvantovej teórie
• Miloslav Dušek: Koncepční otázky kvantové teorie

Exam:
- written test (5points) plus optional oral examination
- solution of homework problems (1 problem = 1 point = 1p)

Evaluation: A>4p, B>3p, C>2p, D>1p, E>0p, F otherwise

Kolokvium:
- solution of homework problems
- hand-written essay