  We consider one-way quantum state merging and entanglement distillation under
compound and arbitrarily varying source models. Regarding quantum compound
sources, where the source is memoryless, but the source state an unknown member
of a certain set of density matrices, we continue investigations begun in the
work of Bjelakovi\'c et. al. [Universal quantum state merging, J. Math. Phys.
54, 032204 (2013)] and determine the classical as well as entanglement cost of
state merging. We further investigate quantum state merging and entanglement
distillation protocols for arbitrarily varying quantum sources (AVQS). In the
AVQS model, the source state is assumed to vary in an arbitrary manner for each
source output due to environmental fluctuations or adversarial manipulation. We
determine the one-way entanglement distillation capacity for AVQS, where we
invoke the famous robustification and elimination techniques introduced by R.
Ahlswede. Regarding quantum state merging for AVQS we show by example, that the
robustification and elimination based approach generally leads to suboptimal
entanglement as well as classical communication rates.
