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arXiv:2608.03262

Analysis of Superradiance-Based Quantum Metrology under Independent Markovian Pure Dephasing

Yasunari Sakuma, Yuichiro Matsuzaki, Hoi-Kwan Lau, Junko Ishi-Hayase

quant-phSubmitted Aug 4, 2026• Announced Aug 5, 2026• 0 citations
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Abstract

Recently, a DC magnetometry protocol utilizing $N$-spin-ensemble superradiance was proposed. This method physically amplifies the acquired signal, suppressing estimation errors from measurement noise and achieving $\mathcal{O}(1/N)$ precision scaling when measurement noise dominates quantum fluctuations. However, quantum metrology is generally vulnerable to independent Markovian pure dephasing. For instance, the scaling of Greenberger-Horne-Zeilinger (GHZ) state-based magnetometry deteriorates from $\mathcal{O}(1/N)$ to $\mathcal{O}(1/\sqrt{N})$. Although pure dephasing likely degrades superradiant sensing, its quantitative impact remains unclear. Here, we investigate the effect of independent Markovian pure dephasing on this protocol using numerical simulations and mean-field analysis. We demonstrate that, in the large-$N$ limit, the estimation error increase is limited to a constant factor. This sharply contrasts with GHZ-state-based sensing, where the error increases by a factor of $\sqrt{N}$. Our analytical solutions elucidate the physical origin of this robustness qualitatively. These findings establish the high robustness of superradiance-based DC magnetometry against independent Markovian pure dephasing.

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The goal of quantum metrology is the precise estimation of parameters using quantum properties such as entanglement. This estimation usually consists of three steps: state preparation, time evolution during which information of the parameters is encoded in the state, and readout of the state. Decoherence during the time evolution typically degrades the performance of quantum metrology and is considered to be one of the major obstacles to realizing entanglement-enhanced sensing. We show, however, that under suitable conditions, this decoherence can be exploited to improve the sensitivity. Assume that we have two axes, and our aim is to estimate the relative angle between them. Our results reveal that the use of Markovian collective dephasing to estimate the relative angle between the two directions affords Heisenberg-limited sensitivity. Moreover, our protocol based on Markovian collective dephasing is robust against environmental noise: it is possible to achieve the Heisenberg limit by applying the collective dephasing even under the effect of independent dephasing. Our counterintuitive proposal with the decoherence leads to alternative applications in quantum metrology.
Abstract Exploring the quantum advantages of various non-classical quantum states in noisy environments is a central subject in quantum sensing. Here we provide a complete picture for the frequency estimation precision of three important states (the Greenberger–Horne–Zeilinger (GHZ) state, the maximal spin squeezed state, and the spin coherent state) of a spin-S under both individual dephasing and collective dephasing by general Gaussian noise, ranging from the Markovian limit to the extreme non-Markovian limit. Whether or not the noise is Markovian, the spin coherent state is always worse than the classical scheme under collective dephasing although it is equivalent to the classical scheme under individual dephasing. Moreover, the maximal spin squeezed state always give the best sensing precision (and outperforms the widely studied GHZ state) in all cases. This establishes the general advantage of the spin squeezed state for noisy frequency estimation in many quantum sensing platforms.
The Heisenberg limit is the superior precision available by entanglement sensors. However, entanglementis fragile against dephasing, and there is no known quantum metrology protocol that can achieve Heisenberg limited sensitivity with the presence of independent dephasing. Here, we show that the Heisenberg limit is attainable under the effect of independent dephasing under conditions where the probe qubits decohere due to both target fields and local environments. To detect the target fields, we exploit the entanglement properties to decay much faster than the classical states due to collective noise while most of the previous schemes use a coherent phase shift from the target fields. Actually, if the temporally fluctuating target fields behave as Markovian collective dephasing, we can estimate the collective dephasing rate with a sensitivity at the Heisenberg limit under the effect of independent dephasing. Our work opens the possibility for robust Heisenberg-limited metrology.
Entanglement is a resource to improve the sensitivity of quantum sensors. In an ideal case, using an entangled state as a probe to detect target fields, we can beat the standard quantum limit by which all classical sensors are bounded. However, since entanglement is fragile against decoherence, it is unclear whether entanglement-enhanced metrology is useful in a noisy environment. Its benefit is indeed limited when estimating the amplitude of dc magnetic fields under the effect of parallel Markovian decoherence, where the noise operator is parallel to the target field. In this paper, on the contrary, we show an advantage to using an entanglement over the classical strategy under the effect of parallel Markovian decoherence when we try to detect ac magnetic fields. We consider a scenario to induce a Rabi oscillation of the qubits with the target ac magnetic fields. Although we can, in principle, estimate the amplitude of the ac magnetic fields from the Rabi oscillation, the signal becomes weak if the qubit frequency is significantly detuned from the frequency of the ac magnetic field. We show that, by using the Greenberger-Horne-Zeilinger (GHZ) states, we can significantly enhance the signal of the detuned Rabi oscillation even under the effect of parallel Markovian decoherence. Our method is based on the fact that the interaction time between the GHZ states and ac magnetic fields scales as 1/L1/L1/L to mitigate the decoherence effect, where LLL is the number of qubits, which contributes to improving the bandwidth of the detectable frequencies of the ac magnetic fields. Our results pave the way for new applications of entanglement-enhanced ac magnetometry.
Most matter-wave interferometry (MWI) schemes for quantum sensing have so far been evaluated in ideal situations without noise. In this work, we provide assessments of generic multiqubit MWI schemes under Markovian dephasing noise. We find that, for certain classes of the MWI schemes with scale factors that are nonlinearly dependent on the interrogation time, the optimal precision of maximally entangled probes decreases with increasing particle number NNN, for both independent and collective dephasing situations. This result challenges the conventional wisdom found in dephasing Ramsey-type interferometers. We initiate the analyses by investigating the optimal precision of multiqubit Sagnac atom interferometry for rotation sensing. And we show that, due to the competition between the unconventional interrogation-time quadratic phase accumulation and the exponential dephasing processes, the Greenberger--Horne--Zeilinger (GHZ) state, which is the optimal input state in noiseless scenarios, leads to vanishing quantum Fisher information in the large-NNN regime. Then our assessments are further extended to generic MWI schemes for quantum sensing with entangled states and under decoherence. Finally, a quantum error-correction logical GHZ state is tentatively analyzed, which could have the potential to recover the Heisenberg scaling and improve the sensitivity.
Dephasing noise is a ubiquitous source of decoherence in current atomic sensors. We address the problem of entanglement-assisted frequency estimation subject to classical dephasing noise with full spatial correlations (collective) and arbitrary temporal correlations. Our contributions are threefold. (i) We derive rigorous, state-independent bounds on the achievable estimation precision, showing how they are entirely determined by the short-time behavior of the decoherence function. For temporally uncorrelated (Markovian) dephasing, precision is limited by a probe-independent constant. For temporally correlated stationary noise, the bound approaches the noiseless limit for classical states, precluding any asymptotic quantum advantage. (ii) We show that these scaling bounds are tight, by constructing generalized Ramsey protocols that saturate them. These optimal protocols use squeezing at the input and before readout, both of which are available in state-of-the-art atomic interferometers. Implementing a perfect-echo protocol, which reaches Heisenberg scaling in the absence of noise, remains optimal in this noisy setting, irrespective of the noise temporal correlations. (iii) We prove that arbitrary collective open-loop control cannot lift the no-go for super-classical precision scaling under either Markovian or colored stationary noise, highlighting the detrimental nature of full spatial correlations. In the latter case, temporal correlations may nonetheless enable constant-factor improvements over the standard quantum limit, which may still be important in practical metrological scenarios.