Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources

Abstract: 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.