• Accepted Paper

Dynamical characterization of quantum coherence

Hai Wang and Ujjwal Sen

Phys. Rev. A - Accepted 4 November, 2026

DOI: https://doi.org/10.1103/t4qy-j4pk

Abstract

Quantum coherence is a fundamental resource in quantum technologies, yet its dynamical role remains elusive. Here, we introduce the average quantum distance to quantify how coherence governs quantum evolution. For time-independent Hamiltonians, we prove that coherence equals the average evolution speed over all energy-level permutations, establishing a direct equivalence between coherence and dynamics. Further, through the famous Stinespring representation, we extend the considerations to open quantum dynamics cases. In addition, real dynamical processes are also included. Beyond this average setting, we show how quantum coherence and the eigenvalues of the Hamiltonian together determine the instantaneous evolution speed in the general case, with the trade-off being the energy uncertainty. We believe that the results clarify the role of quantum coherence in quantum dynamics, paving an alternate avenue, complementary to the existing ones, to understand the capacity of quantum resources in dynamical processes.

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