  Quantum channels model many physical processes. For this reason, hypothesis
testing between quantum channels is a fundamental task in quantum information
theory. Here we consider the paradigmatic case of channel position finding,
where the aim is to determine the position of a target quantum channel within a
sequence of background channels. We explore this model in the setting of
bosonic systems, considering Gaussian channels with the same transmissivity (or
gain) but different levels of environmental noise. Thus the goal of the problem
becomes detecting the position of a target environment among a number of
identical background environments, all acting on an input multi-mode system. We
derive bounds for the ultimate error probability affecting this multi-ary
discrimination problem and find an analytic condition for quantum advantage
over protocols involving classical input states. We also design an explicit
protocol that gives numerical bounds on the ultimate error probability and
often achieves quantum advantage. Finally, we consider direct applications of
the model for tasks of thermal imaging (finding a warmer pixel in a colder
background) and quantum communication (for localizing a different level of
noise in a sequence of lines or a frequency spectrum).
