  We show that the concept of bipartite fluctuations F provides a very
efficient tool to detect quantum phase transitions in strongly correlated
systems. Using state of the art numerical techniques complemented with
analytical arguments, we investigate paradigmatic examples for both quantum
spins and bosons. As compared to the von Neumann entanglement entropy, we
observe that F allows to find quantum critical points with a much better
accuracy in one dimension. We further demonstrate that F can be successfully
applied to the detection of quantum criticality in higher dimensions with no
prior knowledge of the universality class of the transition. Promising
approaches to experimentally access fluctuations are discussed for quantum
antiferromagnets and cold gases.
