One-shot assisted distillation of coherence via one-way local quantum-incoherent operations and classical communication

We obtain the general formula for the optimal rate on one of the subsystems that can be distilled from any bipartite quantum state by one-way local quantum-incoherent operations and classical communication. We provide lower and upper bounds on the assisted distillation of coherence using so-called one-shot entropies, and we establish a hierarchy of information quantities that can be used to calculate an assisted distillable rate in the asymptotical limit. We show that they asymptotically coincide with the quantum-incoherent relative entropy, and our findings imply a novel operational interpretation of quantum-incoherent relative entropy.