Maximal Bell Violations with Predetermined Observables

Abstract

Alice and Bob make independent measurements for non-identical properties. If every Alice (or Bob) event is fixed for any choice of measurement by Bob (or Alice), can they violate a Bell-type inequality? In theory, the answer is negative if all the properties are measured at the same time. However, the answer is positive if only one pair of events is recorded in each iteration. This fact is not widely acknowledged, though often discussed at specialized conferences, because it does not seem to make sense. The overlooked nuance is that staggered events allow for pairwise combinations that are not possible for simultaneous coincidences. This can be illustrated with two synchronized “wheel-of-fortune” tables, while focusing on the patterns of coincidence between consecutive (rather than simultaneous) events.