In quantum physics, one such application is the use of causal inference to certify quantumness in various scenarios, through violations of Bell-like inequalities. This connection puts quantum physicists in a unique position to contribute back to classical causal inference, by addressing open problems whose resolution also benefits quantum applications. In this talk, I will present different examples of such contributions.

I begin by focusing on the marginalized directed acyclic graph (mDAG), a graphical structure developed to study causal structures with latent variables. I will present a new result showing that mDAGs capture exactly the experimentally distinguishable features of such structures: two causal structures can be distinguished by some (possibly intervention-based) experiment if and only if they are associated with different mDAGs.

I then look at the case where interventions are not possible (i.e., only passive observations are available), asking what can still be inferred about the underlying causal structure in this case. Among other conclusions, the results of this investigation will highlight that causal compatibility constraints that take the form of inequalities - which are central to quantum physicists interested in causal inference - are also important for classical causal inference.

Finally, I will present recent work on estimating the quantitative parameters of a causal model from observational data, in a form of “classical self-testing”. We believe the ideas developed here may also inform future efforts to quantify causal influence in quantum causal structures.