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This paper addresses a fundamental challenge in quantum metrology by deriving bandwidth thresholds for distinguishing thermal noise modes when coupling spectra are unknown, offering protocols that utilize fractional-clock sampling and calibrated pulse widths to exclude common-temperature fits. The study provides rigorous theoretical and numerical acquisition guarantees for binary-readout protocols designed to handle Gaussian oscillator loss and readout drift without requiring mode-resolved access. These findings advance the precision of quantum-noise measurements, which is critical for developing robust quantum sensors and communication systems.
Thermal aliases in quantum noise: sampling clocks and pulse widths
arXiv:2610.16889v1 Announce Type: new Abstract: Can collective quantum-noise measurements distinguish different mode temperatures from one common temperature when the coupling spectrum is unknown? For stationary Gaussian oscillator environments, we derive a sharp bandwidth threshold for an exact thermal alias on the integer-time sampling lattice. The threshold depends on temperature order through the quantum response. For frequencies within the first alias period, fixing sufficient integer-time correlations makes one additional fractional-time fluctuation observation enough to exclude every common-temperature fit. A calibrated second pulse width provides another route through the same collective port: both widths must probe one spectrum and retain their measured variance scales. For a specified two-mode example, continuous-frequency certificates cover all common temperatures and uncertainty in a shared pulse ramp. A binary-readout protocol combines randomly interleaved matched references with collective-variance and coherence checks to handle Gaussian oscillator loss and predictable readout drift. The selected fractional-clock and two-width designs require approximately $3.8\times10^7$ and $1.6\times10^8$ outcomes for at most 5\% type-I error and at least 95\% power on the stated alternative class. These theoretical and numerical acquisition guarantees assume independently validated preparation, spectral support and control specifications; validation costs are additional. The result identifies which new observation makes thermal-model testing informative when mode-resolved access is unavailable.
Abstract:Can collective quantum-noise measurements distinguish different mode temperatures from one common temperature when the coupling spectrum is unknown? For stationary Gaussian oscillator environments, we derive a sharp bandwidth threshold for an exact thermal alias on the integer-time sampling lattice. The threshold depends on temperature order through the quantum response. For frequencies within the first alias period, fixing sufficient integer-time correlations makes one additional fractional-time fluctuation observation enough to exclude every common-temperature fit. A calibrated second pulse width provides another route through the same collective port: both widths must probe one spectrum and retain their measured variance scales. For a specified two-mode example, continuous-frequency certificates cover all common temperatures and uncertainty in a shared pulse ramp. A binary-readout protocol combines randomly interleaved matched references with collective-variance and coherence checks to handle Gaussian oscillator loss and predictable readout drift. The selected fractional-clock and two-width designs require approximately $3.8\times10^7$ and $1.6\times10^8$ outcomes for at most 5\% type-I error and at least 95\% power on the stated alternative class. These theoretical and numerical acquisition guarantees assume independently validated preparation, spectral support and control specifications; validation costs are additional. The result identifies which new observation makes thermal-model testing informative when mode-resolved access is unavailable.
Quantum Physics (quant-ph); Computational Physics (physics.comp-ph)
arXiv:2610.16889 [quant-ph]
(or arXiv:2610.16889v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.16889 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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