Kinetic Uncertainty Relations (KURs) establish quantum transport precision limits by linking signal-
to-noise ratio (SNR) to the system’s dynamical activity, valid in the weak-coupling regime where
particle-like transport dominates. At strong coupling, quantum coherence challenges the validity of
KURs and questions the concept of activity itself. In this Letter, we achieve two distinct, yet
complementary main results. First, we introduce a general definition of dynamical activity valid at
arbitrary coupling, which reveals the breakdown of standard KURs at strong coupling. Second, we
prove a novel uncertainty relation valid at arbitrary coupling strength, which we denote Quantum
KUR (QKUR). This QKUR corresponds to a nontrivial quantum extension of KUR, involving
fundamental contributions of the generalized dynamical activity. These two achievements provide a
general framework for out-of-equilibrium quantum transport precision analysis, in close analogy with
the transition from TURs to QTURs [Phys. Rev. Lett. 135, 046302]. Explicit steady-state expressions
are obtained within Green’s-function and Landauer-Büttiker formalisms. We illustrate these concepts
for paradigmatic quantum-coherent mesoscopic devices: a single quantum channel pinched by a
quantum point contact and open single- and double-quantum dot systems.
