Optimizing the Sensitivity-Noise Trade-off in Non-Hermitian Sensing via Off-Exceptional-Deficiency Operation

Abstract:A central challenge in non-Hermitian sensing is that spectral singularities simultaneously amplify both the signal and environmental noise. We address this predicament in a double-chain Hatano-Nelson model featuring unidirectional interlayer coupling. At the exceptional deficiency (ED) limit, the system exhibits a macroscopically degenerate complex spectrum and a pronounced non-Hermitian skin effect (NHSE), yielding a sensitivity that scales exponentially with lattice size $N$ while remaining robust across a six-order-of-magnitude detuning range. By introducing diagonal spatial disorder, we demonstrate that the NHSE is progressively suppressed, whith eigenspace cosine similarity analysis quantifying a well-defined fault-tolerance threshold. To reconcile the sensitivity-noise trade-off, we delineate "At-ED" and "Off-ED" operating regimes. While the At-ED configuration imposes fractional-order noise amplification (SNR $\propto \delta^{-1/2}$) that saturates at a suboptimal plateau, migrating to the Off-ED regime eliminates this geometric singularity and restores a linear scaling law (SNR $\propto \delta^{-1}$), achieving an SNR enhancement of several orders of magnitude. Crucially, this improvement is achieved while fully preserving the exponential sensitivity scaling, albeit at a slightly reduced absolute sensitivity compared to the strict At-ED limit. Our findings establish the Off-ED framework as a concrete paradigm for next-generation topological sensors that reconcile extreme sensitivity with robust noise immunity.

arXiv:2606.04386 [quant-ph]

(or arXiv:2606.04386v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.04386 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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