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# Nonlocal games and operator algebras: solution spaces and robust self-testing in the quantum commuting model

# Nonlocal games and operator algebras: solution spaces and robust self-testing in the quantum commuting model

#### Speaker: Alexander Frei (University of Copenhagen)

## Abstract

We begin by recalling quantum strategies in the context of nonlocal games, and their description in terms of the state space on the full group algebra of certain free groups. With this description at hand, we then examine the quantum value and quantum strategies for the following prominent classes of games:
1) The tilted CHSH game.
We showcase here how to compute the quantum value at first for the classical CHSH game using some basic operator algebraic techniques. For the more general tilted CHSH game, we then invoke some more elaborate classification of representations which then allows us to reduce the quantum value to an optimisation problem. These allow us moreover to deduce the solution space of optimal states and their uniqueness, in the sense that there will be only a single optimal state giving rise to the optimal quantum value, and which in particular entails the usual self-testing result. We moreover find previously unknown phase transitions on the uniqueness of optimal states when varying the parameters for the tilted CHSH game.
2) The Mermin-Peres magic square and magic pentagram game.
As before, we also note here uniqueness of optimal states, which in these two examples is a basically familiar result.
Based on uniqueness of optimal states as entire states on full group algebras, we then discuss robust self-testing in the quantum commuting model in the context of above discussed games. We do so by building upon ideas found in work by Mancinska, Prakash and Schafhauser. We then demonstrate this on the classes (1) and (2) above, and so find a first robust self-testing result in the quantum commuting model.
The talk is based on joint work with Azin Shahiri.

Opublikowano przez Pawel Mazurek

Date: środa, 29 czerwca, 2022

Time: 15:15

Location: Quantum Information and Quantum Computing Working Group (CTP PAS)

Zoom link: https://us06web.zoom.us/j/87850698108

Passcode: nisq

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