Precision limits for time-dependent quantum metrology under Markovian noise

• URL: http://arxiv.org/abs/2605.18392v1
• Date: Mon, 18 May 2026 13:39:22 GMT
• Title: Precision limits for time-dependent quantum metrology under Markovian noise
• Abstract summary: We derive ultimate precision bounds for estimating parameters encoded in emphtime-dependent Hamiltonians in the presence of general Markovian noise.<n>We illustrate these behaviors on paradigmatic driven-qubit sensors, exhibiting $T4$ and $T3$ scalings under dephasing and spontaneous emission.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive ultimate precision bounds for estimating parameters encoded in \emph{time-dependent} Hamiltonians in the presence of general Markovian noise, allowing for arbitrary adaptive protocols with fast controls and noiseless ancillas. Extending the minimization-over-purifications framework to time-varying continuous channels, we obtain a differential upper bound on the achievable quantum Fisher information (QFI) that can be evaluated at all times via semidefinite programming. For parameter-independent noise, we prove a universal long-time scaling law: if the coherent (noiseless) dynamics yields $Q_{\mathrm{coh}}(T)\sim T^{2k}$, then under Markovian noise the QFI scales at most as $Q(T)\sim T^{2k}$ in the DHNLS regime, whereas in the DHLS regime it is fundamentally limited to $Q(T)\sim T^{2k-1}$. We illustrate these behaviors on paradigmatic driven-qubit sensors, exhibiting $T^{4}$ and $T^{3}$ scalings under dephasing and spontaneous emission, respectively. Finally, we provide explicit continuous exact and approximate quantum error correction constructions -- supplemented by spin-squeezed probes -- that asymptotically saturate the bounds, establishing their tightness.

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