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arXiv:2605.18392

Precision limits for time-dependent quantum metrology under Markovian noise

Luca Previdi, Francesco Albarelli

quant-phSubmitted May 18, 2026• Announced May 19, 2026• 0 citations
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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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Quantum metrology promises precision beyond classical limits, yet environmental noise typically degrades the quantum resources required for such enhancement. In this work, we investigate frequency estimation in noisy continuous-variable systems, focusing on two complementary strategies to mitigate decoherence: Hamiltonian engineering and the exploitation of non-Markovian dynamics. By embedding squeezing directly into the system Hamiltonian, we show that the quantum Fisher information (QFI) may acquire a tunable higher-order time dependence, leading to enhanced sensitivity in the short-time regime. Moving beyond the Markovian approximation, we employ the quantum Brownian motion model to demonstrate that structured environments with finite memory can induce information backflow, temporarily restoring and even improving estimation precision relative to the unitary limit. We further assess the achievability of these bounds via Gaussian measurements, identifying regimes where homodyne, heterodyne, and optimized general-dyne measurements saturate the QFI, and noting that stronger squeezing widens the gap, potentially requiring non-Gaussian measurement strategies. Our results establish that jointly tailoring system Hamiltonian and environmental memory offers a viable route toward robust quantum-enhanced frequency estimation in open systems.