Causal links between operationally independent events in quantum theory

In any known description of nature, two physical systems are considered independent of each other if any action on one of the systems does not change the other system. From our classical intuitions about the world, we further conclude that these two systems are not affecting each other in any possible way, and thus these two systems are causally disconnected or they do not influence each other. Building on this idea, we show that in quantum theory such a notion of “classical independence” is not satisfied, that is, two quantum systems can still influence each other even if any operation on one of the systems does not create an observable effect on the other. For our purpose, we consider the framework of quantum networks and construct a linear witness utilizing the Clauser-Horne-Shimony-Holt inequality. We also discuss one of the interesting applications resulting from the maximal violation of classical independence towards device-independent certification of quantum states and measurements.

Figure 1

Weak-bilocality scenario. Alice and Bob each receive a single particle from their respective sources, which might be correlated to each other, while Eve receives two particles, one from each of these sources. Alice and Bob have the freedom to independently select and conduct two dichotomic measurements on their respective particles. In contrast, Eve's measurement is constrained to a single four-outcome measurement. None of the parties can communicate with each other.

Figure 2

Causality graph of the weak-bilocality scenario. The square boxes represent the measurement devices and the circles represent the sources. The gray circle represents a hidden variable that might correlate the sources.