  Discrimination between objects, in particular quantum states, is one of the
most fundamental tasks in (quantum) information theory. Recent years have seen
significant progress towards extending the framework to point-to-point quantum
channels. However, with technological progress the focus of the field is
shifting to more complex structures: Quantum networks. In contrast to channels,
networks allow for intermediate access points where information can be
received, processed and reintroduced into the network. In this work we study
the discrimination of quantum networks and its fundamental limitations. In
particular when multiple uses of the network are at hand, the rooster of
available strategies becomes increasingly complex. The simplest quantum network
that capturers the structure of the problem is given by a quantum superchannel.
We discuss the available classes of strategies when considering $n$ copies of a
superchannel and give fundamental bounds on the asymptotically achievable rates
in an asymmetric discrimination setting. Furthermore, we discuss achievability,
symmetric network discrimination, the strong converse exponent, generalization
to arbitrary quantum networks and finally an application to an active version
of the quantum illumination problem.
