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arXiv · 2608.19761

Krylov Tomography and Finite-Uncertainty Certification of Exceptional-Point Dynamics

Aritra Ghosh·M. Bhattacharya
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Abstract

Exceptional points (EPs) can produce striking responses, but locating one does not reveal how much of its dynamics an excitation accesses, which responses a detector distinguishes, or whether a missing signal is absent or undetected. We introduce Krylov tomography, a preparation- and measurement-aware framework that uses time-resolved data and models with stated uncertainty limits to answer these questions, while also bounding offset-induced departures from exact-EP behavior. As an explicit illustration of the general framework, we present finite-precision simulations of a red-sideband optomechanical model, whose second-moment coherence sector contains a third-order EP, certifying preparation-sensitive access to two and three directions. Krylov tomography thus bridges EP structure and finite-precision measurements, providing a general framework for non-Hermitian systems.

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Aritra Ghosh, M. Bhattacharya. 2026-08-20. Krylov Tomography and Finite-Uncertainty Certification of Exceptional-Point Dynamics. https://arxiv.org/abs/2608.19761

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