Universität Wien

260017 VU The maths and the physics of space-like quantum correlations (2022W)

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

  • Wednesday 12.10. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 19.10. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 09.11. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 16.11. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 23.11. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 30.11. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 07.12. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 14.12. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 11.01. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Wednesday 18.01. 10:00 - 12:30 Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien

Information

Aims, contents and method of the course

As observed by Bell, the measurement statistics (or correlations) generated by two or more separate observers probing a joint quantum system do not admit, in general, a classical explanation. Hence, a single quantum experiment is enough to rule out all classical theories. This result, Bell’s theorem, is just a hint of how special quantum correlations are: as we will see in this course, quantum correlations are so bizarre that they even allow ruling out classical theories with faster-than-light interactions. They also rule out real quantum mechanics, a version of quantum theory where all bras and kets have real entries. Quantum correlations are a pain to work with, as any attempt to characterize them quickly runs into undecidable problems. We will study mathematical and physical principles that limit the set of quantum correlations, and conclude that correlations in any future theory superseding quantum physics cannot be very different from quantum (although there is room for surprises!).

Assessment and permitted materials

Home exercises and a final oral test.

Minimum requirements and assessment criteria

The final grade will be the result of averaging the scores of two series of exercises (30%) and a final test (70%).

Examination topics

1. Classical correlations

a) Bell’s theorem. Characterization of Bell nonlocality.

b) The no-signalling set. Hidden variable models with secret communication.

2. Quantum correlations

a) The limits of quantum correlations: Tsirelson’s bound. XOR games.

b) The characterization of quantum boxes. Tsirelson’s problem, undecidability and the NPA hierarchy.

3. Classifying general physical theories by their correlations.

a) Physical sets of correlations. Closure under wirings: definition, properties, examples.

b) Do we expect correlations to be very different from quantum? Five device-independent physical principles to constrain physical correlations: no-trivial communication complexity, no-advantage for nonlocal computation, information causality, macroscopic locality and local orthogonality.

c) The limitations of the black-box approach: the almost-quantum set of correlations.

3. Quantum correlations in networks. Falsifying real quantum theory.

Reading list

1. B. Lang, T. Vértesi, M. Navascués, Closed sets of correlations: answers from the zoo, Journal of Physics A 47, 424029 (2014).
2. J.-D. Bancal, S. Pironio, A. Acín, Y.-C. Liang, V. Scarani, N. Gisin, Quantum nonlocality based on finite-speed causal influences leads to superluminal signaling, Nature Physics 8, 867 (2012).
3. G. Brassard, H. Buhrman, N. Linden, A. A. Methot, A. Tapp and F. Unger, F., Limit on Nonlocality in Any World in Which Communication Complexity Is Not Trivial, Phys. Rev. Lett., 96 250401, (2006).
4. M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, Information Causality as a physical principle, Nature 461, 1101 (2009).
5. M. Navascués and H. Wunderlich, A glance beyond the quantum model, Proc. Royal Soc. A 466:881-890 (2009).
6. T. Fritz, A. B. Sainz, R. Augusiak, J. B. Brask, R. Chaves, A. Leverrier and A. Acín, Local orthogonality as a multipartite principle for quantum correlations, Nature Communications 4, 2263 (2013).
7. M. Navascués, Y. Guryanova, M. Hoban and A. Acín, Almost quantum correlations. Nat Commun 6, 6288 (2015).
8. M.O. Renou, D. Trillo, M. Weilenmann et al., Quantum theory based on real numbers can be experimentally falsified, Nature 600, 625–629 (2021).

Association in the course directory

M-VAF A 2, M-VAF B

Last modified: We 05.10.2022 13:10