  As an analogy of fully entangled fraction in the framework of entanglement
theory, we have introduced the notion of quantum coherence fraction
$C_{\mathcal{F}}$, which quantifies the closeness between a given state and the
set of maximally coherent states. By providing an alternative formulation of
the robustness of coherence $C_{\mathcal{R}}$, we have elucidated the
relationship between quantum coherence fraction and the normalized version of
$C_{\mathcal{R}}$ (i.e., $\overline{C}_{\mathcal{R}}$), where the role of
genuinely incoherent operations (GIO) is highlighted. Numerical simulation
shows that though as expected $C_{\mathcal{F}}$ is upper bounded by
$\overline{C}_{\mathcal{R}}$, $C_{\mathcal{F}}$ constitutes a good
approximation to $\overline{C}_{\mathcal{R}}$ especially in low-dimensional
Hilbert spaces. Even more intriguingly, we can analytically prove that
$C_{\mathcal{F}}$ is exactly equivalent to $\overline{C}_{\mathcal{R}}$ for
qubit and qutrit states. Moreover, some intuitive properties and implications
of $C_{\mathcal{F}}$ are also indicated.
