Can we think time-symmetrically about causation?

We often say that quantum mechanics allows to calculate the probability of future events. In fact, quantum mechanics does not discriminate between predicting the future or postdicting the past. I will present the results of a recent work by Rovelli, Donà and me, where we address the apparent tension between the time symmetry of elementary quantum mechanics and the intrinsic time orientation of the formulations of quantum theory used in the quantum information and foundations communities. Additionally, I will sketch a way to think time symmetrically about causality in quantum theory by using the new notion of a causal-inferential theory recently proposed by Schimd, Selby and Spekkens.