Imitation games and C*-algebras

02/03/2018, 14:00 - 15:00 in MAP/0G/018

Ivan Todorov (Queen’s University Belfast)


Abstract:

There has been a substantial recent interaction between two-player one-round games (also knows as non-local games) and Quantum Information Theory. On one hand, these games may serve as a test for the presence of entanglement, while on the other, entanglement and related resources can lead to improved strategies for the players. Connections between non-local games and two major open problems – the Tsirelson problem in Quantum Physics and the Connes Embedding Problem in Operator Algebra Theory – have led to the solution of the weak Tsirelson problem by Slofstra in 2016 and a further alternative solution by Dykema, Paulsen and Prakash in 2017, and have confirmed their importance in both fields.

In this talk, I will introduce the new class of imitation games, which includes as special cases the games utilised by Slofstra and Dykema-Paulsen-Prakash. I will describe a way to associate a C*-algebra to each such game, and will relate the winning quantum strategies for such a game to the traces on the corresponding C*-algebra. In the case the interest lies in strategies beyond quantum – such as generalised probabilistic ones – I will highlight the insufficiency of C*-algebra techniques and the need to pass to the more general framework of operator systems.