Assisted Coherence Distillation of Certain Mixed States

We study the assisted coherence distillation of two special classes of mixed states including the states with vanished basis-dependent discord in the incoherent basis of the second party and Werner two-qubit states via the sets of operations such as local incoherent operations and classical communication (LICC), local quantum-incoherent operations and classical communication (LQICC), separable incoherent operations (SI), and separable quantum-incoherent operations (SQI). We show that the assisted distillable coherence of the former can reach the upper bound, namely quantum-incoherent (QI) relative entropy via all the sets of operations considered above. In contrast, for the Werner two-qubit states the assisted distillable coherence is strictly smaller than the quantum-incoherent (QI) relative entropy. Our results also mean that the optimal rate of assisted coherence distillation of Werner two-qubit states can be achieved even in one-copy scenarios without the complex joint quantum operations on many copies. Finally, we discuss the coherence location in the multipartite system.