Optimizing the Sensitivity-Noise Trade-off in Non-Hermitian Sensing via Off-Exceptional-Deficiency Operation
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Quantum Physics arXiv:2606.04386 (quant-ph) [Submitted on 3 Jun 2026] Title:Optimizing the Sensitivity-Noise Trade-off in Non-Hermitian Sensing via Off-Exceptional-Deficiency Operation Authors:Shangxuan Li, Bin Guo View a PDF of the paper titled Optimizing the Sensitivity-Noise Trade-off in Non-Hermitian Sensing via Off-Exceptional-Deficiency Operation, by Shangxuan Li and Bin Guo View PDF HTML (experimental) 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. Subjects: Quantum Physics (quant-ph) Cite as: 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) Submission history From: Bin Guo [view email] [v1] Wed, 3 Jun 2026 03:02:32 UTC (7,023 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimizing the Sensitivity-Noise Trade-off in Non-Hermitian Sensing via Off-Exceptional-Deficiency Operation, by Shangxuan Li and Bin GuoView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)