  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.
