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Lecture: Foundations of Quantum Mechanics

Lecturer: David Gross. Exercises: Mariami Gachechiladze, Lukas Franken

Course description

The course will cover the properties of quantum mechanics that are fundamentally different from any classical theory. This contrasts with the usual QM classes, where the goal is to treat specific systems; and with Quantum Information Theory, where the focus lies on ways to exploit quantum behavior for computation and communication.

Topics are:

  • Contextuality, Bell inequalities, and "quantum non-locality"
  • Causality and its interaction with quantum probability
  • Uncertainty relations and their interpretation
  • The problem of joint measurability
  • No-cloning
  • Generalized Probabilistic Theories, post-quantum correlations and their convex geometry
  • Measurement theory and decoherence
  • Projective representations of symmetries

Language is English, despite what Ilias says (don't know how to change that...)



The lecture will take place online. Video recordings will be provided. The lecture is good for 6 ECTS points and will fit into the GR/QFT and the CM/CP areas of specialization.

There will be Zoom online meetings:

  • Every Monday at 4pm with the lecturer David Gross
  • Every Tuesday at 4pm with the exercise team Mariami Gachechiladze and Lukas Franken

Next lecture meeting: Monday, 6th of July, 4.00pm. Click here to join Zoom meeting.

The recap meeting: Wednesday, July 22nd, 4pm. Click here to join Zoom meeting. (Tuesday does not work for me!)

For exercises and general communication it is highly recommended to join the Slack-Channel, which is set up for organization of all master lectures' tutorials offered by the Institute for Theoretical Physics. Click here to join! Mail addresses associated with Universitites Cologne and Bonn can join automatically, for access with your private mail, please contact Lukas Franken.

Exam Standards

For those taking an exam, here's what we expect. We will not ask for topics listed as "not relevant", but won't mind talking about them if you bring them up.

  • Definition of non-contextual distributions, significance, examples, quantum violations
  • Everything about the CHSH inequality
  • The "impossible machines"
  • For a perfect grade: State-independent contextuality, loopholes, Tisrelson's bound
  • Not: Klyachko's Pentagram proof, the more philosophical aspects of the notion of "elements of reality"
  • Be able to qualitatively talk about the non-signalling polytope
  • For perfect grade: Be somewhat comfotable with the basic notions of convexity introduced
  • Not: The computer code to find dual descriptions of convex bodies; obviously don't have to memorize vertices / facets or such details; The "too kinky to be real" lecture
  • Mixed states (where they come from and how they are described mathematically)
  • POVMs: definition, one or two examples, statement of Naimark's dilation theorem.
  • For perfect grade: Unambiguous state discrimination and POVMs
  • Quantum operations: Problem statement, complete positivity, Kraus representation
  • For perfect grade: Be able to discuss partial transpose map
  • Not: Proofs of the dilation theorems, philosophical issues around the measurement problem
  • Not: The long essay we read in Week 11


Using this link, you can access the contents of the whiteboard. Videos can be accessed via direct links below, or via the Vimeo showcase. Password is "quantum", with "qu" replaced by "kw" (to discourage scrapping).


Solutions to all discussed exercises.

Week 1

Further Reading

Week 2

Further reading

Week 3

Further Reading


Week 4

Announcement: Previous videos used 1k (or "full HD") resolution. All following videos are available in 4k. If you have sufficient bandwith, make sure to select 4k by clicking on the cogwheel.

Further Reading

Week 5

Further Reading

Week 6

Further Reading


Week 7

Further Reading

Week 8


Week 9


Week 10

Further reading:


Week 11