Mixed-state coherence quantification and channel-based estimation based on Hellinger distance

Abstract As a core resource for quantum advantage, quantum coherence plays a crucial role in the precise quantification of quantum information processing. In this work, we investigate the quantification problem of quantum coherence based on Hellinger distance. For quantum systems, we derive analytical expressions for the coherence measurement of two types of mixed states (maximum coherent mixed state and block diagonal state) based on Hellinger distance and identify their closest incoherent states. By applying these theoretical results, we solve the problem of distinguishing pure state ensembles. In addition, mixed permutation channels were used to estimate the Hellinger distance coherence of certain quantum states and provide an analytical lower bound for coherence. Therefore, to some extent, it avoids complex calculations in high-dimensional Hilbert spaces. We hope that this study can promote further research on coherence theory based on the Hellinger distance framework.