  The search for a simple description of fundamental physical processes is an
important part of quantum theory. One example for such an abstraction can be
found in the distance lab paradigm: if two separated parties are connected via
a classical channel, it is notoriously difficult to characterize all possible
operations these parties can perform. This class of operations is widely known
as local operations and classical communication (LOCC). Surprisingly, the
situation becomes comparably simple if the more general class of separable
operations is considered, a finding which has been extensively used in quantum
information theory for many years. Here, we propose a related approach for the
resource theory of quantum coherence, where two distant parties can only
perform measurements which do not create coherence and can communicate their
outcomes via a classical channel. We call this class local incoherent
operations and classical communication (LICC). While the characterization of
this class is also difficult in general, we show that the larger class of
separable incoherent operations (SI) has a simple mathematical form, yet still
preserving the main features of LICC. We demonstrate the relevance of our
approach by applying it to three different tasks: assisted coherence
distillation, quantum teleportation, and single-shot quantum state merging. We
expect that the results obtained in this work also transfer to other concepts
of coherence which are discussed in recent literature. The approach presented
here opens new ways to study the resource theory of coherence in distributed
scenarios.
