Quantum Kinetic Uncertainty Relations in Mesoscopic Conductors at Strong Coupling

TL;DR

This paper introduces a quantum extension of kinetic uncertainty relations (KURs) for mesoscopic conductors at strong coupling, accounting for quantum coherence and providing new bounds on current fluctuations.

Contribution

It develops a generalized dynamical activity concept valid at any coupling strength, leading to the Quantum KUR (QKUR) that extends classical bounds to quantum coherent regimes.

Findings

Standard KURs break down at strong coupling due to quantum coherence.

The generalized activity reduces to classical definitions in weak coupling.

QKUR provides tighter bounds on current fluctuations in quantum dot systems.

Abstract

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, particle-like 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.