Seminar on nonlocal games

Julien Schanz

Prof. Dr. Moritz Weber

Supported by: Simon Schmidt

Contents

In this seminar we will learn about nonlocal games in the realm of quantum information theory. Typically, a nonlocal game is played by Alice and Bob supervised by a referee. The players are not allowed to communicate but they might share an entangled state. In some situations, sharing such an entangled state leads to better chances to win the game which can be seen as an instance of "quantum supremacy".

We will treat some basics in quantum information theory before coming to a number of examples of nonlocal games. Depending on the participants, we might also dig deeper into functional analytic aspects such as C*-algebras or quantum symmetries related to nonlocal games. However, there are no prerequisites for the seminar. For some talks, it might help to have a background in functional analysis, but the seminar will also be accessible without this background.

The seminar is held in English unless all participants speak German.

Talks

• (1) 9.11., YN, [MW]. The mathematics of quantum information theory 1 (Pure/mixed/entangled states, partial trace, Schmidt decomposition) [Aubrun-Szarek, Ch. 2.1.1, parts of Ch. 2.2; Watrous Ch. 2.1]
• (2) 16.11., AL, [MW]. The mathematics of quantum information theory 2 (Entanglement) [Aubrun-Szarek, parts of Ch. 2.2; Watrous, parts of Ch. 6]
• (3) 23.11., ASC, [MW]. The mathematics of quantum information theory 3 (Quantum channels, Stinespring representation) [Aubrun-Szarek Ch. 2.3; Watrous Ch. 2.2]
• (4) 30.11., MK, [MW]. The mathematics of quantum information theory 4 (Quantum measurement, POVM, correlations) [Nielsen-Chuang Ch. 2.2.3-2.2.6, Watrous Ch. 2.3]
• (5) 7.12., DZ, [SSch]. CHSH game
• (6) 14.12., LS, [SSch]. Synchronous games
• (7) 11.1., NF, [SSch]. Pseudo telepathy games
• (8) 18.1., NB, [JSch]. Magic squares and linear binary constraint systems
• (9) 25.1., EO, [JSch]. Graph isomorphism game, quantum isomorphisms of graphs 1
• (10) 1.2., ST, [JSch]. Graph isomorphism game, quantum isomorphisms of graphs 2
• (11) 8.2., LJ, [MW]. NN.

[JSch] = supervised by Julien Schanz; [SSch] = supervised by Simon Schmidt; [MW] = supervised by Moritz Weber.

If you feel uncomfortable giving your talk in English, please indicate to us. Please contact the organizers of the
seminar before preparing your talk. The talks are shall be prepared for 60 minutes (but your slot is 90 minutes
- it includes time for questions and discussions).

The talk may or may not include an ``Ausarbeitung'', depending on your study regulations and the amount of
credit points you aim for.