Quantum coherence fraction

As an analogy of the fully entangled fraction in the framework of entanglement theory, we have introduced the notion of quantum coherence fraction C-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-R, we have elucidated the relationship between the quantum coherence fraction and the normalized version of C-R, i.e., (C) over bar (R), where the role of genuinely incoherent operations is highlighted. Numerical simulation shows that, though as expected C-F is upper bounded by (C) over bar (R), C-F constitutes a good approximation to (C) over bar (R) especially in low-dimensional Hilbert spaces. Even more intriguingly, we can analytically prove that C-F is exactly equivalent to (C) over bar (R) for qubit and qutrit states. Moreover, some intuitive properties and implications of C-F are also indicated.