Contextuality Revisited: Signaling May Differ From Communicating

Abstract

The notion of contextuality in quantum theory expresses that the result of a measurement (e.g. performed by Alice) depends on the experimental context or, more precisely, on other measurements (e.g. performed by Bob). This kind of contextuality presupposes that signals transferring information about Bob’s experiment to Alice (and vice versa) are excluded. In quantum physics this can be guaranteed if the two measurements are performed within the causal complements of their lightcones. In this case, signaling would violate special relativity. Some recent scenarios in cognitive science apply a similar non-signaling condition to test whether measurements on cognitive systems are contextual. For a refined discussion of contextuality in such scenarios, we argue that it is important to distinguish two types of signaling: (1) signaling that Alice and Bob can use to communicate, and (2) signaling that Alice and Bob cannot use to communicate. Lacking communication may be inconclusive for contextuality if signaling without communication is still present.