IQI Weekly Seminar
Abstract: Given a non-local game, a basic question is: how much entanglement is required to play optimally? If we allow commuting-operator strategies, then playing optimally can require an infinite-dimensional Hilbert space. This follows from a stronger result: for any finitely-presented group G, there is a non-local game which forces the players to implement a representation of G to play perfectly. This stronger result is potentially very useful for designing self-testing / device-independent scenarios. However, there is a catch, in that even if G has finite-dimensional representations, the game constructed might not have a perfect strategy outside of the commuting-operator framework.
In this talk, I will show that for many groups it is possible to construct non-local games which require a representation of G to be played perfectly, and which can be played perfectly on a limit of finite-dimensional strategies. In particular, this will allow us to construct non-local games which can be played perfectly with a limit of finite-dimensional strategies, but cannot be played perfectly with any fixed finite-dimensional strategy. This also opens up the possibility of self-testing a wide range of groups.