260017 VU The maths and the physics of space-like quantum correlations (2022W)
Prüfungsimmanente Lehrveranstaltung
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- Anmeldung von Do 01.09.2022 08:00 bis Mo 26.09.2022 07:00
- Abmeldung bis Fr 21.10.2022 23:59
Details
max. 15 Teilnehmer*innen
Sprache: Englisch
Lehrende
Termine (iCal) - nächster Termin ist mit N markiert
Mittwoch
12.10.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
19.10.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
09.11.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
16.11.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
23.11.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
30.11.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
07.12.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
14.12.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
11.01.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Mittwoch
18.01.
10:00 - 12:30
Seminarraum, Zi. 3354A, Boltzmanngasse 5, 3. Stk., 1090 Wien
Information
Ziele, Inhalte und Methode der Lehrveranstaltung
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!).
Art der Leistungskontrolle und erlaubte Hilfsmittel
Home exercises and a final oral test.
Mindestanforderungen und Beurteilungsmaßstab
The final grade will be the result of averaging the scores of two series of exercises (30%) and a final test (70%).
Prüfungsstoff
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.
Literatur
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).
Zuordnung im Vorlesungsverzeichnis
M-VAF A 2, M-VAF B
Letzte Änderung: Mi 05.10.2022 13:10