Speaker: Georgios Baziotis, University of Delaware

Title: Measurable No-signalling Correlations

Abstract: A non-local game is one where two players play cooperatively against a referee, trying to convince the latter of the joint possession of a certain predescribed knowledge, without any in-game communication allowed. In the case where the two players do not possess a perfect strategy, the optimal winning probability and its asymptotic version become essential. In this talk, we consider the infinite parallel repetition of a finite game as a single infinite game and introduce the notion of a measurable no signalling correlation by replacing finite sets with second countable compact Hausdorff spaces and families of POVMs with operator-valued information channels.  We define the measurable counterparts of various classes of no-signalling correlations and focus on the quantum spatial and quantum commuting. To that end, we establish two measurable versions of Stinespring's Dilation Theorem. Finally, we define values of measurable non-local games of local, quantum spatial and quantum commuting type, and show how the asymptotic value of a finite game can be achieved as a special case of the inner value of a measurable game. Based on joint work with Ivan Todorov and Lyudmila Turowska.