Quantum coherence fraction
Yao Yao, Dong Li, C. P. Sun · Physical Review A · 2019
As an analogy of the 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 the quantum coherence fraction and the normalized version of ${C}_{\mathcal{R}}$, i.e., ${\overline{C}}_{\mathcal{R}}$, where the role of genuinely incoherent operations 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.