Nonlocal games with synchronous correlations

Brad Lackey, University of Maryland

A nonlocal game with a synchronous correlation is the ideal protocol for quantum key distribution. In this work we examine analogues of Bell's inequalities for synchronous correlations. We show that unlike in the nonsynchronous case (e.g. with the CHSH inequality) there can be no quantum Bell violation among synchronous correlations with two measurement settings. However we exhibit explicit analogues of Bell's inequalities for synchronous correlation with three measurement settings and two outputs that do admit quantum violations. We also provide an analogue of Tsirl'son's bound in this setting, exhibit this bound is sharp, and prove rigidity of the quantum states achieving the bound.