Coherence of assistance and regularized coherence of assistance

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.

Figure 1

Quantum states in this polyhedron satisfy four inequalities: $r_1+r_2+r_3+1\ge 0$, $r_1-r_2-r_3+1\ge 0$, $r_2-r_1-r_3+1\ge 0$, and $r_3-r_1-r_2+1\ge 0$. The coherence of assistance attains the regularized coherence of assistance for these quantum states.