Advanced Quantum Theory

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.

Topics include:

• 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.

 

Literature:

General literature:

• 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:

Lecture 1:

Nielsen and Chuang, Chapter 2.2

Lecture 2:

Many useful lecture notes: google for "lecture notes second quantization"

Lecture 3:

Nielsen and Chuang, Chapter 2.4

Lecture 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 

Lecture 5:

Nielsen and Chuang, Chapter 8.2

Lecture notes of Norbert Schuch

Lecture 6:

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

Lecture 7

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

Lecture 8:

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

Lectures 9/10:

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.

Lecture 11:

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.