Non-Hermitian Sensing via a Divergent Quantum Metric

The quantum metric, a geometric measure of state-space distance, has recently attracted growing attention for capturing anomalous state responses to parameter variations. Especially in non-Hermitian systems, the quantum metric has been observed to diverge when the eigenstates coalesce, a phenomenon identified as a remarkable resource for sensing. Here, by exploiting this divergence, we establish a non-Hermitian sensing scheme that leverages enhanced transient dynamics to provide a geometric gain for amplifying external field signals. We confirm the critical enhancement in the Fisher information using a trapped-ion 171Yb+ platform and demonstrate superior noise robustness over conventional eigenvalue-splitting--based non-Hermitian schemes by evaluating the minimum detectable signal. Moreover, this scheme can be naturally combined with non-Hermitian topological dynamics, revealing a unique unidirectional sensing response, which indicates its potential for directional signal discrimination. Our work establishes a new paradigm for sensing in open quantum systems through critical quantum geometry and opens a route toward robust topological quantum sensing.