Non-Kolmogorov-Arnold-Moser Quantum Sensors for Quantum Parameter Estimation
Abstract
Non-KAM (Kolmogorov-Arnold-Moser) systems, when subjected to weak time-dependent perturbations, exhibit an abrupt transition to classical chaos through the breakdown of invariant phase-space tori. We showcase the utilization of non-KAM systems in the quantum regime as quantum sensors, leveraging their sensitivity at \textit{resonances}. Quantum Fisher information (QFI) is a central quantity in quantum parameter estimation theory that measures how much information a quantum state contains about an unknown parameter that is encoded into it. In other words, it quantifies the sensitivity of a quantum state to small changes in that parameter. In this work, through numerical analysis in conjunction with analytical results, we study the performance of the non-KAM systems for quantum sensing applications by computing the QFI. We find that the growth of the QFI is remarkably enhanced when the resonance condition is satisfied. For frequency estimation under Floquet unitary encodings, we derive a transport bound: if the mean excitation number grows as ⟨n̂(t)⟩∼ tα, the QFI obeys I(t)≲ t2α+2. The quantum kicked harmonic oscillator, a paradigmatic non-KAM system, realizes the full hierarchy: localized dynamics (α=0) yield quadratic growth, delocalized diffusion along stochastic webs (α=1) yields quartic growth, and translationally invariant resonances (α=2) saturate the bound with anomalous hexic growth, I(t)∼ t6, established analytically at resonance R=2 and numerically at R=4. The enhancement stems from resonance-induced translational symmetry rather than exponential instability, identifying non-KAM resonances as a metrological resource distinct from chaos-assisted and criticality-based sensing.
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BibTeX
@misc{varikuti2026nonkolmogorovarnoldmoser,
title = {{Non-Kolmogorov-Arnold-Moser Quantum Sensors for Quantum Parameter Estimation}},
author = {Naga Dileep Varikuti and Sourav Manna and Athreya Shankar and Arul Lakshminarayan and Vaibhav Madhok},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03092},
eprint = {2609.03092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03092},
}
RIS
TY - UNPB
TI - Non-Kolmogorov-Arnold-Moser Quantum Sensors for Quantum Parameter Estimation
AU - Naga Dileep Varikuti
AU - Sourav Manna
AU - Athreya Shankar
AU - Arul Lakshminarayan
AU - Vaibhav Madhok
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03092
UR - https://arxiv.org/abs/2609.03092
AB - Non-KAM (Kolmogorov-Arnold-Moser) systems, when subjected to weak time-dependent perturbations, exhibit an abrupt transition to classical chaos through the breakdown of invariant phase-space tori. We showcase the utilization of non-KAM systems in the quantum regime as quantum sensors, leveraging their sensitivity at \textit{resonances}. Quantum Fisher information (QFI) is a central quantity in quantum parameter estimation theory that measures how much information a quantum state contains about an unknown parameter that is encoded into it. In other words, it quantifies the sensitivity of a quantum state to small changes in that parameter. In this work, through numerical analysis in conjunction with analytical results, we study the performance of the non-KAM systems for quantum sensing applications by computing the QFI. We find that the growth of the QFI is remarkably enhanced when the resonance condition is satisfied. For frequency estimation under Floquet unitary encodings, we derive a transport bound: if the mean excitation number grows as ⟨n̂(t)⟩∼ t^α, the QFI obeys I(t)≲ t^2α+2. The quantum kicked harmonic oscillator, a paradigmatic non-KAM system, realizes the full hierarchy: localized dynamics (α=0) yield quadratic growth, delocalized diffusion along stochastic webs (α=1) yields quartic growth, and translationally invariant resonances (α=2) saturate the bound with anomalous hexic growth, I(t)∼ t^6, established analytically at resonance R=2 and numerically at R=4. The enhancement stems from resonance-induced translational symmetry rather than exponential instability, identifying non-KAM resonances as a metrological resource distinct from chaos-assisted and criticality-based sensing.
ER -