  We introduce one-way LOCC protocols for quantum state merging for compound
sources, which have asymptotically optimal entanglement as well as classical
communication resource costs. For the arbitrarily varying quantum source (AVQS)
model, we determine the one-way entanglement distillation capacity, where we
utilize the robustification and elimination techniques, well-known from
classical as well as quantum channel coding under assumption of arbitrarily
varying noise. Investigating quantum state merging for AVQS, we demonstrate by
example, that the usual robustification procedure leads to suboptimal resource
costs in this case.
