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

摘要

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