Quantum Kinetic Uncertainty Relations in Mesoscopic Conductors at Strong Coupling

Kinetic uncertainty relations (KURs) set fundamental limits on the precision of nonequilibrium transport by bounding the signal-to-noise ratio of currents in terms of the dynamical activity, a quantity that counts exchange events between a system and its reservoirs. This framework is well established in the weak-coupling regime, where transport occurs via well-defined, particlelike tunneling processes. At strong coupling, however, quantum coherence challenges both the validity of standard KURs and the notion of activity itself. In this Letter, we introduce a generalized definition of dynamical activity valid at arbitrary system-reservoir coupling, and show that it leads to a breakdown of standard KURs at strong coupling. Building on this result, we derive and prove a novel uncertainty relation, denoted quantum KUR (QKUR), which provides a genuine quantum extension of KUR, accounting for intrinsic quantum coherent contributions of the generalized activity. We demonstrate that the generalized activity reduces to the standard master-equation definition in the weak-coupling regime for generic systems of N coupled quantum dots described by a quadratic Hamiltonian, and analyze the resulting QKUR bound in paradigmatic quantum-coherent mesoscopic devices, including single- and double-quantum dot systems and a quantum point contact.