Approximate distillation of quantum coherence

Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this paper, we develop the framework of the approximate coherence distillation under strictly incoherent operations. This protocol considers the situation that we cannot transform an initial state $\rho$ into a target state $\psi$ with certainty; instead, we aim to deterministically transform the initial state $\rho$ into an intermediate state $\phi$ that is most approximate to the target state $\psi$ in terms of fidelity. We also present the explicit conversion strategy of the approximate coherence distillation.