Multi-round Box

Abstract

In the previous chapter we discussed the single-round box, which can be seen as a simple abstract object that allows us to study the fundamental aspects of non-locality. When studying actual device-independent information processing tasks, however, one must consider more complex objects that describe the behaviour of the devices while performing the task of interest. More concretely, in actual applications we usually interact with a device by playing many games. Even in the simplest setting where one would like to merely verify the violation of a Bell inequality, as in experiments performing loophole-free Bell tests, a Bell game is played many times so that sufficient amount of data can be collected to estimate the violation in a satisfactory statistical manner. Playing just a single game is clearly not enough. Another example is device-independent protocols, such as quantum key distribution. All protocols include a phase in which the users (or honest parties) are playing many games with their device in order to decide whether it can be used for the considered task. Hence, considering boxes that can be used to play just a single game is not enough. Instead, we need to work with multi-round boxes.