Introduction to quantum games and their values I
The theory of non-local games, rooted in Bell’s seminal work on non-locality, is at the forefront of entanglement theory and has revealed profound connections with non-commutative analysis. Examples of quantum non-local games have been studied, wherein quantum states and/or measurements are used in place of classical questions and/or answers, but a general theory has only recently begun to emerge. This developing theory and its potential applications increase the necessity to avail of a systematic way of comparing essential attributes of distinct quantum games, in particular, their values, i.e., maximum success probabilities. In this sequence of talks we will introduce a (large) class of quantum non-local games and present our operator space resource theoretic approach to computing their values. In particular, we establish new tensor norm expressions for a number important resources, including entanglement assisted local operations in the commuting operator framework, and local operations and one-way classical communication. This is based on joint work with Rupert Levene, Ivan Todorov and Lyudmila Turowska.