Accessible coherence and coherence distribution

The definition of accessible coherence is proposed. Through local measurement on the other subsystem and one-way classical communication, a subsystem can access more coherence than the coherence of its density matrix. Based on the local accessible coherence, the part that cannot be locally accessed is also studied, which we call it remaining coherence. We study how the bipartite coherence is distributed by partition for both $l_1$ norm coherence and relative entropy coherence, and the expressions for local accessible coherence and remaining coherence are derived. We also study some examples to illustrate the distribution.

Figure 1

The distribution of coherence for the ground state of (26) with relative entropy measure (a) and the $l_1$ norm measure (b). At $J/\lambda =0$, for both relative entropy coherence and $l_1$ norm coherence, the local coherence ($C_{A\left(B\right)}^r$ and $C_{A\left(B\right)}^{l_1}$, blue dots) and local accessible coherence ($C_{A\left(B\right)}^{{\mathcal{A}}^r}$ and $C_{A\left(B\right)}^{{\mathcal{A}}^{l_1}}$, green dots) are all zero, and the bipartite coherence ($C^r$ and $C^{l_1}$, black dots) is just the remaining coherence ($C^{{\mathcal{T}}^r}$ and $C^{{\mathcal{T}}^{l_1}}$, red dots). At $J/\lambda \to \infty$, for the relative entropy coherence, the local accessible coherence and the remaining coherence approach to zero. And all the bipartite coherence is from the local coherence. While for the $l_1$ norm coherence the remaining coherence is nonzero, and the bipartite coherence is distributed into both local coherence and the remaining coherence.