  Causal influences are at the core of any empirical science, the reason why
its quantification is of paramount relevance for the mathematical theory of
causality and applications. Quantum correlations, however, challenge our notion
of cause and effect, implying that tools and concepts developed over the years
having in mind a classical world, have to be reevaluated in the presence of
quantum effects. Here, we propose the quantum version of the most common
causality quantifier, the average causal effect (ACE), measuring how much a
target quantum system is changed by interventions on its presumed cause. Not
only it offers an innate manner to quantify causation in two-qubit gates but
also in alternative quantum computation models such as the measurement-based
version, suggesting that causality can be used as a proxy for optimizing
quantum algorithms. Considering quantum teleportation, we show that any pure
entangled state offers an advantage in terms of causal effects as compared to
separable states. This broadness of different uses showcases that, just as in
the classical case, the quantification of causal influence has foundational and
applied consequences and can lead to a yet totally unexplored tool for quantum
information science.
