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arXiv:2410.01881 · Physical Review Letters

Universal Bounds for Quantum Metrology in the Presence of Correlated Noise

Stanisław Kurdziałek, Francesco Albarelli, Rafał Demkowicz-Dobrzański

Published Jul 31, 2025• 5 citations
arXivHTMLPDF

Abstract

We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations (mathematically described by quantum combs), which may be effectively computed in the limit of a large number of probes or sensing channels involved. Although the bounds are not guaranteed to be tight in general, their tightness may be systematically increased by increasing the numerical complexity of the procedure. Interestingly, this approach yields bounds tighter than the state of the art also for uncorrelated channels. We apply the bounds to study the limits for the most general adaptive phase estimation models in the presence of temporally correlated dephasing. We consider dephasing both parallel (no Heisenberg scaling) and perpendicular (Heisenberg scaling possible) to the signal. In the former case our new bounds show that negative correlations are beneficial; for the latter we show evidence that the bounds are tight. We also apply the bounds to collisional thermometry, i.e., estimation of a parameter of the environment, showing evidence that entangled probes may provide only a limited advantage.

DOI
10.1103/jy3v-wkcb

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We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations (mathematically described by quantum combs), which may be effectively computed in the limit of a large number of probes or sensing channels involved. Although the bounds are not guaranteed to be tight in general, their tightness may be systematically increased by increasing the numerical complexity of the procedure. Interestingly, this approach yields bounds tighter than the state of the art also for uncorrelated channels. We apply the bounds to study the limits for the most general adaptive phase estimation models in the presence of temporally correlated dephasing. We consider dephasing both parallel (no Heisenberg scaling) and perpendicular (Heisenberg scaling possible) to the signal. In the former case our new bounds show that negative correlations are beneficial; for the latter we show evidence that the bounds are tight. We also apply the bounds to collisional thermometry, i.e., estimation of a parameter of the environment, showing evidence that entangled probes may provide only a limited advantage.
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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 Qcoh(T)∼T2kQ_{\mathrm{coh}}(T)\sim T^{2k}Qcoh​(T)∼T2k, then under Markovian noise the QFI scales at most as Q(T)∼T2kQ(T)\sim T^{2k}Q(T)∼T2k in the DHNLS regime, whereas in the DHLS regime it is fundamentally limited to Q(T)∼T2k−1Q(T)\sim T^{2k-1}Q(T)∼T2k−1. We illustrate these behaviors on paradigmatic driven-qubit sensors, exhibiting T4T^{4}T4 and T3T^{3}T3 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.