  Heisenberg's uncertainty principle implies fundamental constraints on what
properties of a quantum system can we simultaneously learn. However, it
typically assumes that we probe these properties via measurements at a single
point in time. In contrast, inferring causal dependencies in complex processes
often requires interactive experimentation - multiple rounds of interventions
where we adaptively probe the process with different inputs to observe how they
affect outputs. Here we demonstrate universal uncertainty principles for
general interactive measurements involving arbitrary rounds of interventions.
As a case study, we show that they imply an uncertainty trade-off between
measurements compatible with different causal dependencies.
