Operational Meaning of Dynamical Total Coherence in Single-Parameter Quantum Channel Estimation

Abstract

We establish the rigorous operational meaning of dynamical total coherence within the resource non-increasing (RNI) framework for the task of single-parameter quantum channel estimation. By connecting distance-based and maximal-increment-based dynamical coherence measures with the right-logarithmic-derivative (RLD) Fisher information and the Cramér-Rao bound (CRB), we prove that each dynamical coherence measure directly determines the fundamental precision limit of channel parameter estimation. We show that the diamondnorm measure yields a tight error lower bound, the induced trace-norm measure gives a simplified bound for device-limited scenarios, the relative-entropy measure governs the asymptotic error-exponent rate, the l 2 -based measure quantifies the precision gain from optimal input states, and the RLD-Fisher-based measure provides an achievable error upper bound. This work unifies dynamical resource theory with quantum channel estimation and endows dynamical total coherence with clear, task-oriented operational significance.