  Learning a hidden property of a quantum system typically requires a series of
interactions. In this work, we formalise such multi-round learning processes
using a generalisation of classical-quantum states, called classical-quantum
combs. Here, "classical" refers to a random variable encoding the hidden
property to be learnt, and "quantum" refers to the quantum comb describing the
behaviour of the system. The optimal strategy for learning the hidden property
can be quantified by applying the comb min-entropy (Chiribella and Ebler, NJP,
2016) to classical-quantum combs. To demonstrate the power of this approach, we
focus attention on an array of problems derived from measurement-based quantum
computation (MBQC) and related applications. Specifically, we describe a known
blind quantum computation (BQC) protocol using the combs formalism and thereby
leverage the min-entropy to provide a proof of single-shot security for
multiple rounds of the protocol, extending the existing result in the
literature. Furthermore, we consider a range of operationally motivated
examples related to the verification of a partially unknown MBQC device. These
examples involve learning the features of the device necessary for its correct
use, including learning its internal reference frame for measurement
calibration. We also introduce a novel connection between MBQC and quantum
causal models that arises in this context.
