  The topic of causality has recently gained traction quantum information
research. This work examines the problem of single-shot discrimination between
process matrices which are an universal method defining a causal structure. We
provide an exact expression for the optimal probability of correct distinction.
In addition, we present an alternative way to achieve this expression by using
the convex cone structure theory. We also express the discrimination task as
semidefinite programming. Due to that, we have created the SDP calculating the
distance between process matrices and we quantify it in terms of the trace
norm. As a valuable by-product, the program finds an optimal realization of the
discrimination task. We also find two classes of process matrices which can be
distinguished perfectly. Our main result, however, is a consideration of the
discrimination task for process matrices corresponding to quantum combs. We
study which strategy, adaptive or non-signalling, should be used during the
discrimination task. We proved that no matter which strategy you choose, the
probability of distinguishing two process matrices being a quantum comb is the
same.
