Introduction to Quantum Theory
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
QNIE-UKT | Z,ZK | 6 | 2P+2C | English |
- Course guarantor:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Applied Mathematics
- Synopsis:
-
interpretation of quantum theory are explained using simple models mainly from finite-dimensional quantum mechanics. Emphasis is placed on further applications of quantum theory to information processing and communication. Possible physical realizations of a qubit, description of multipartite systems, quantum entanglement and its applications are discussed. The course concludes with a description of continuous quantum systems in infinite-dimensional Hilbert spaces, in particular the linear harmonic oscillator as a description of the mode of a quantized electromagnetic field.
- Requirements:
- Syllabus of lectures:
-
1.Historical introduction, experiments leading to quantum theory, motivation for quantum information processing.
2.Mathematical apparatus of quantum theory - properties of finite-dimensional Hilbert spaces, Hermitian and unitary operators.
3.Interference of probability amplitudes - double-slit experiment, Mach-Zehnder interferometer.
4. Two-level systems - spin-1/2 as a model of qubit model, Bloch sphere, photon polarization.
5. Observables, predictions of measurement results.
6. Influence of measurement on quantum state, incompatibility and uncertainty relations.
7. Time evolution of a quantum system, Schroedinger equation, evolution operator.
8. Deity matrices, pure and mixed states..
9. Description of multipartite quantum systems, separable and entangled states.
10. Quantum entanglement - Bell states, Schmidt decomposition, nonlocality, GHZ state.
11. Quantum teleportation.
12. Bell's inequalities, criteria and measures of entanglement.
13. Quantum harmonic oscillator, energy eigenstates, creation and annihilation operators, coherent states.
- Syllabus of tutorials:
-
1.Historical introduction, experiments leading to quantum theory, motivation for quantum information processing.
2.Mathematical apparatus of quantum theory - properties of finite-dimensional Hilbert spaces, Hermitian and unitary operators.
3.Interference of probability amplitudes - double-slit experiment, Mach-Zehnder interferometer.
4. Two-level systems - spin-1/2 as a model of qubit model, Bloch sphere, photon polarization.
5. Observables, predictions of measurement results.
6. Influence of measurement on quantum state, incompatibility and uncertainty relations.
7. Time evolution of a quantum system, Schroedinger equation, evolution operator.
8. Deity matrices, pure and mixed states..
9. Description of multipartite quantum systems, separable and entangled states.
10. Quantum entanglement - Bell states, Schmidt decomposition, nonlocality, GHZ state.
11. Quantum teleportation.
12. Bell's inequalities, criteria and measures of entanglement.
13. Quantum harmonic oscillator, energy eigenstates, creation and annihilation operators, coherent states.
- Study Objective:
-
interpretation of quantum theory are explained using simple models mainly from finite-dimensional quantum mechanics. Emphasis is placed on further applications of quantum theory to information processing and communication. Possible physical realizations of a qubit, description of multipartite systems, quantum entanglement and its applications are discussed. The course concludes with a description of continuous quantum systems in infinite-dimensional Hilbert spaces, in particular the linear harmonic oscillator as a description of the mode of a quantized electromagnetic field.
- Study materials:
-
1. Feynman, R. P., Leighton, R. B., Sands, M.: Feynmanovy přednášky z fyziky - revidované vydání 3. díl
Fragment 2013
ISBN 978-80-253-1644-3
2. Dušek, M.: Koncepční otázky kvantové teorie
UP, Olomouc 2002
ISBN 80-244-0449-4
3. Barnett, S.: Quantum Information
Oxford University Press 2009
ISBN 9780198527633
- Note:
-
The course is presented in English.
- Further information:
- https://courses.fit.cvut.cz/QNIE-UKT
- No time-table has been prepared for this course
- The course is a part of the following study plans: