Advanced Quantum Theory
Lecturer: PD Dr. Martin Gärttner
Link to LSF
This lecture gives an introduction to quantum information theory and theory of open quantum systems. The lecture is accompanied by exercises and bi-weekly tutorials.
- Recap of basic quantum mechanics: Postulates, qubit systems, density matrix
- Quantum measurement
- Quantum entanglement
- Schmidt decomposition and purifications
- EPR paradox and Bell inequalities
- Quantum channels
- Distance measures between quantum states
- Classical and quantum entropy
- Quantum thermalization
- Lindblad Master equation
Dates and rooms: Lecture Mondays 14:15-16:00 starting on 25.04.2022. Room: Philos.-weg 12 / kHS. Tutorials biweekly on Tuesdays 14:15-16:00 or Wednesdays 14:15-16:00.
Prerequisites: Solid knowledge of quantum mechanics (PEP3+PTP4). Theoretical Quantum Statistics or Introduction to Quantum Science and Technology is very useful.
Mode of examination: The grade will be based on a written exam.
- Nielsen and Chuang: Quantum Computation and Quantum Information (Classic textbook. We will focus on the quantum information part) http://mmrc.amss.cas.cn/tlb/201702/W020170224608149940643.pdf
- Watrous: The Theory of Quantum Information (Comprehensive introduction to quantum information theory, rather formal/mathematical, including some more specialized concepts) https://cs.uwaterloo.ca/~watrous/TQI/
- Wilde: From Classical to Quantum Shannon Theory (Very comprehensive introduction to classical and quantum information theory, focus on coding and data compression, data transmission) https://arxiv.org/abs/1106.1445
- Lecture notes by John Preskill: http://theory.caltech.edu/~preskill/ph219/index.html#lecture(Chapters 1-4 and 10) and corresponding videos: https://www.youtube.com/playlist?list=PL0ojjrEqIyPy-1RRD8cTD_lF1hflo89Iu
Specific literature for each lecture:
Nielsen and Chuang, Chapter 2.2
Many useful lecture notes: google for "lecture notes second quantization"
Nielsen and Chuang, Chapter 2.4
Lecture notes of Norbert Schuch: https://www.quantuminfo.physik.rwth-aachen.de/cms/Quantuminfo/Studium/QI-Kurse/Vorherige-Kurse/~jifv/Quantum-Information-SS15-/lidx/1/
specifically Chapter "Formalism": https://www.quantuminfo.physik.rwth-aachen.de/global/show_document.asp?id=aaaaaaaaaamtkaw
Nielsen and Chuang, Chapter 8.2
Lecture notes of Norbert Schuch
Qubit channels: Nielsen and Chuang, Chapter 8.3
Lindblad Master equation: Lecture notes of Gernot Schaller, Chapter 1: https://www1.itp.tu-berlin.de/schaller/download/TOQT.pdf
Nielsen and Chuang, Chapter 2.6
Pedagogical paper on Bell inequalities: https://aapt.scitation.org/doi/pdf/10.1119/1.4823600
Original EPR paper: https://journals.aps.org/pr/abstract/10.1103/PhysRev.47.777
Original paper by J. Bell: https://journals.aps.org/ppf/abstract/10.1103/PhysicsPhysiqueFizika.1.195
Original CHSH paper: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.23.880
First experimental violation of Bell inequality: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.47.460
Loophole free experimental test: https://www.nature.com/articles/nature15759
Nielsen and Chuang, Chapter 12.5
Review article on entanglement: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.81.865
Review article on entanglement measures: https://arxiv.org/abs/quant-ph/0504163
Nielsen and Chuang, Chapter 11
Note that there is a sign error in lecture notes 10: In the proof of subadditivity, in the second line, there should be a minus sign in front of S(rho_AB). The subsequent line is correct again.
Nielsen and Chuang, Chapter 12.1
Review article: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Luca D'Alessio,Yariv Kafri, Anatoli Polkovnikov and Marcos Rigol. https://arxiv.org/abs/1509.06411
The lecture materials will be uploaded here.
- sheet Problem set 1
- sheet Problem set 2
- sheet Problem set 3
- sheet Problem set 4
- sheet Problem set 5
- sheet Problem set 6
- Group 1 (Niklas Euler)
INF 227 / SR 3.403, Tue 14:15 - 16:00
- Group 2 (Adrian Aasen)
Philos.-weg 12 / kHS, Wed 14:15 - 16:00
Link zum LSF