Advanced Quantum Theory

Sommersemester 2022
Dozent: PD Dr. Martin Gärttner
Link zum LSF
55 Teilnehmer/innen

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.



General literature:

  • Nielsen and Chuang: Quantum Computation and Quantum Information (Classic textbook. We will focus on the quantum information part)
  • Watrous: The Theory of Quantum Information (Comprehensive introduction to quantum information theory, rather formal/mathematical, including some more specialized concepts)
  • Wilde: From Classical to Quantum Shannon Theory (Very comprehensive introduction to classical and quantum information theory, focus on coding and data compression, data transmission)
  • Lecture notes by John Preskill: 1-4 and 10) and corresponding videos:

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:

specifically Chapter "Formalism": 

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:

Lecture 7

Nielsen and Chuang, Chapter 2.6

Pedagogical paper on Bell inequalities:

Original EPR paper:

Original paper by J. Bell:

Original CHSH paper:

First experimental violation of Bell inequality:

Loophole free experimental test:

Lecture 8:

Nielsen and Chuang, Chapter 12.5

Review article on entanglement:

Review article on entanglement measures:

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.

The lecture materials will be uploaded here.



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Advanced Quantum Theory
Sommersemester 2022
Link zum LSF
55 Teilnehmer/innen