  We study the relation between the coherence of assistance and the regularized
coherence of assistance introduced by Chitambar et al. [E. Chitambar et al.,
Phys. Rev. Lett. 116, 070402 (2016)]. The necessary and sufficient conditions
that these two quantities coincide are provided. Detailed examples are analyzed
and the optimal pure state decompositions such that the coherence of assistance
equals the regularized coherence of assistance are derived. Moreover, we
present the protocol for obtaining the maximal relative entropy coherence,
assisted by another party under local measurement and one-way communication in
one copy setting.

Quantum Physics