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

Continuous assessment of course work

## Labels

## 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).

- Registration is open from
**Th 01.09.2022 08:00**to**Mo 26.09.2022 07:00** - Deregistration possible until
**Fr 21.10.2022 23:59**

## 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

N
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 correlationsa) Bell’s theorem. Characterization of Bell nonlocality.b) The no-signalling set. Hidden variable models with secret communication.2. Quantum correlationsa) 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).

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*