Susceptibility-kinetic uncertainty relations for quantum systems

• URL: http://arxiv.org/abs/2607.01035v1
• Date: Wed, 01 Jul 2026 15:04:17 GMT
• Title: Susceptibility-kinetic uncertainty relations for quantum systems
• Abstract summary: Kinetic uncertainty relations bound current precision of processes by dynamical activity.<n>The extension of these bounds to quantum systems has been impeded by coherence, strong system-reservoir coupling.<n>We show that a partial dynamical activity bounds current precision via a universal susceptibility-kinetic uncertainty relation.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kinetic uncertainty relations bound current precision of stochastic processes by dynamical activity. The extension of these bounds to quantum systems has been impeded by coherence, strong system-reservoir coupling, and the subtlety of defining dynamical activity in the quantum regime. Here, we introduce a partial dynamical activity through the quantum Fisher information associated with the rescaling of the system-reservoir coupling and show that it bounds current precision via a universal susceptibility-kinetic uncertainty relation. The general validity of this relation for any open quantum system is guaranteed by the natural contribution of a susceptibility term, which is experimentally accessible by tuning the system-reservoir coupling strength. We show how the partial dynamical activity encompasses previous definitions of activity in the weak-coupling Markovian limit and that it provides an information-geometric interpretation of correlator-based activities. We illustrate the tight constraint on precision that our bound provides with the example of steady-state transport through a double quantum dot, where quantum effects invalidate previously developed kinetic uncertainty relations. We expect our bound to provide a powerful tool for optimizing precision in arbitrary quantum systems.

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