Introduction to Quantum Theory

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:

Information about the course and teaching materials can be found at https://courses.fit.cvut.cz/QNI-UKT

Further information:

https://courses.fit.cvut.cz/QNI-UKT

No time-table has been prepared for this course

The course is a part of the following study plans:

• Quantum Informatics (compulsory course in the program)