
Selected chapters from quantum mechanics
 Faculty of Informatics, Masaryk University, Brno
 code: IA082
 B411, Wednesdays 18:0019:30
 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 beamsplitter,
√NOT logic gate,
§ 2. Quantum interference and superposition
 doubleslit experiment, MachZender 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
 twolevel quantum system (polarization and spin1/2),
SternGerlach experiments, Bloch sphere, orthogonality and information,
nocloning 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, minentropy
§ 8. EinsteinPodolskiRosen paradox
 composite quantum systems, tensor product, quantum steering,
EPR paradox, local hidden variable model, CHSH inequalities, experiments
and loopholes
§ 9. Quantum onetime pad protocols
 onetime pad, superdense coding and teleportation
§ 10. Quantum entanglement
 correlated and separable states, definition of entanglement,
entanglement distilation,
§ 11. Quantum cryptography
 QKD protocols BB84, E91, noquantum 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
 handwritten essay

