Universität Wien
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260022 VU Probabilistic theories and reconstructions of quantum theory (2023W)

5.00 ECTS (3.00 SWS), SPL 26 - Physik
Continuous assessment of course work
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 15 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

During each lecture day, there will be a suitable break of at least 15 minutes (at around 11:15), or longer if needed.

  • Wednesday 04.10. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 11.10. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 18.10. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 25.10. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 08.11. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 15.11. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 22.11. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 29.11. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 06.12. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 13.12. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 10.01. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 17.01. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Wednesday 24.01. 10:00 - 12:30 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien

Information

Aims, contents and method of the course

Quantum theory is one of our most successful physical theories, but its standard textbook formulation is quite mysterious. For example, why are states described by complex vectors in a Hilbert space, and why do observables correspond to self-adjoint operator? In this lecture, we will see how the formalism of quantum theory can be derived from simple physical or information-theoretic principles. This is similar to the derivation of the Lorentz transformations from the relativity principle and the constancy of the speed of light. To this end, we will study the framework of “generalized probabilistic theories”, which generalizes both classical and quantum probability theory and which has become an indispensable tool in quantum information theory research over the last few years. Students will also gain knowledge of important aspects of convex geometry, duality, and group representation theory which are very useful in other areas of theoretical physics, in particular in quantum information theory.

Assessment and permitted materials

2 homeworks, each accounting for 15% of the grade; a final exam accounts for 70%.

Minimum requirements and assessment criteria

Sufficiently regular attendance of the lectures. Moreover, students must attain at least 50% of the total points on the homeworks and final exam to pass.

Examination topics

Contents of the lecture. See “Aims, Contents and Methods” above, and the topics listed in the Les Houches lecture notes in the reading list below.

Reading list

• M. P. Müller, Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes), SciPost Lect. Notes 28 (2021), arXiv:2011.01286.
• M. Plávala, General probabilistic theories: An introduction, arXiv:2103.07469
• J. Barrett, Information processing in generalized probabilistic theories, Phys. Rev. A 75, 032304 (2007).
• L. Hardy, Quantum Theory From Five Reasonable Axioms, arXiv:quant-ph/0101012.
• Ll. Masanes and M. P. Müller, A derivation of quantum theory from physical requirements, New J. Phys. 13, 063001 (2011).
• R. Webster, Convexity, Oxford University Press, 1994.
• B. Simon, Representations of Finite and Compact Groups, American Mathematical Society, 1996.

Association in the course directory

M-VAF A 2, M-VAF B

Last modified: Mo 25.09.2023 13:48