Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Entanglement-enhanced ac magnetometry in the presence of Markovian noise

Thanaporn Sichanugrist, Hajime Fukuda, Takeo Moroi, Kazunori Nakayama, So Chigusa, Norikazu Mizuochi, M. Hazumi, Yuichiro Matsuzaki

Published Apr 7, 2025• 4 citations
Publisher

Abstract

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 $1/L$ to mitigate the decoherence effect, where $L$ 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.

DOI
10.1103/physreva.111.042605

Related papers

Entanglement-enhanced AC magnetometry in the presence of Markovian noises

Thanaporn Sichanugrist, Hajime Fukuda, Takeo Moroi +5 more

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 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 $1/L$ to mitigate the decoherence effect where $L$ is the number of qubits, which contributes to improving the bandwidth of the detectable frequencies of the AC magnetic fields. Our results open up the way for new applications of entanglement-enhanced AC magnetometry.

arXiv:2410.21699•Oct 29, 2024•0 citations

Quantum magnetometry with superconducting-qubit Greenberger–Horne–Zeilinger and Dicke probes

Azat R. Gubaydullin, Vladimir Slepnev, Alexey Yu. Mironov +1 more

Quantum sensing has become a key technology for precision measurement, with applications spanning magnetometry, gravitational sensing, navigation and geodesy, materials and device diagnostics, and biomedical detection. This motivates the study of quantum-enhanced magnetometry with entangled states. We focus on Greenberger–Horne–Zeilinger (GHZ) and Dicke states operated within a Kitaev phase estimation algorithm (PEA). We consider superconducting fluxonium-qubit sensors, which are modelled with relaxation and dephasing noise. Using a Bayesian update procedure, we evaluate the estimation performance and compare the GHZ and Dicke sensors in terms of sensitivity, dynamical range, and information gain. GHZ probes achieve the highest local sensitivity, while Dicke probes maintain comparable sensitivity over a substantially wider bias interval and exhibit improved tolerance to bias errors and edge effects in PEA sequence. Our results demonstrate a trade-off between local peak sensitivity and the achievable dynamical range and robustness under noise.

Scientific Reports•Aug 14, 2026•0 citations

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

Yasunari Sakuma, Yuichiro Matsuzaki, Hoi-Kwan Lau +1 more

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.

quant-pharXiv:2608.03262•Aug 5, 2026•0 citations

Magnetic field sensing beyond the standard quantum limit under the effect of decoherence

Yuichiro Matsuzaki, Simon C. Benjamin, Joseph F. Fitzsimons

Entangled states can potentially be used to outperform the standard quantum limit by which every classical sensor is bounded. However, entangled states are very susceptible to decoherence, and so it is not clear whether one can really create a superior sensor to classical technology via a quantum strategy which is subject to the effect of realistic noise. This paper presents an investigation of how a quantum sensor composed of many spins is affected by independent dephasing. We adopt general noise models including non-Markovian effects, and in these noise models the performance of the sensor depends crucially on the exposure time of the sensor to the field. We have found that, by choosing an appropriate exposure time within the non-Markovian time region, an entangled sensor does actually beat the standard quantum limit. Since independent dephasing is one of the most typical sources of noise in many systems, our results suggest a practical and scalable approach to beating the standard quantum limit.

arXiv:1101.2561•Physical Review A•Jul 5, 2011•208 citations

Mitigating detuning-induced systematic errors in entanglement-enhanced metrology

Shingo Kukita, Yuichiro Matsuzaki

Quantum sensing leverages non-classical resources to enhance precision. In particular, Greenberger-Horne-Zeilinger (GHZ) states can, in principle, attain the Heisenberg limit that surpasses the standard quantum limit. While many studies have examined how open-system noise-typically modeled with Lindblad master equations-degrades GHZ-based metrology, coherent control imperfections during state preparation and readout have received less attention. Here, we analyze the effect of detuning between actual and nominal spin frequencies in a GHZ-state preparation scheme employing a frequency selective pulse. We show that detuning induces coherent, systematic error that prevents GHZ sensing from reaching the Heisenberg limit. To mitigate this effect, we design a composite-pulse protocol that compensates for detuning-induced errors and improves the sensitivity under the effect of coherent error.

arXiv:2510.16739•Physical Review A•Mar 4, 2026•0 citations

Entanglement Enhanced Sensing with Qubits affected by non-Markovian Dephasing

Noah Kaufmann, Kasper H. Nielsen, Eva M. González-Ruiz +1 more

Entanglement has been proposed as a means to improve the sensitivity of sensing weak signals. While the degree of this quantum advantage is well understood in noiseless settings, the situation is more complex under realistic conditions, where the system is subject to decoherence. In this case, the enhancement depends on the specific noise characteristics. Previous treatments of colored noise typically assume that the noise is uncorrelated between successive experiments. Here, we consider the scenario in which the noise exhibits correlations across multiple shots. We derive a simple fundamental limit to the sensitivity based on the fact that the sensitivity cannot be better than the signal-to-noise ratio seen by the probe. Focusing on Ramsey spectroscopy with probes affected by pure classical dephasing, we show that, for suitable spatial and temporal noise correlations, entangled probes achieve a better scaling of the sensitivity with the number of probes than separable states. This demonstrates that entanglement can provide a substantial improvement for Ramsey spectroscopy subject to correlated noise.

quant-pharXiv:2604.22368•Apr 27, 2026•0 citations
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.
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 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 open up the way for new applications of entanglement-enhanced AC magnetometry.
Quantum sensing has become a key technology for precision measurement, with applications spanning magnetometry, gravitational sensing, navigation and geodesy, materials and device diagnostics, and biomedical detection. This motivates the study of quantum-enhanced magnetometry with entangled states. We focus on Greenberger–Horne–Zeilinger (GHZ) and Dicke states operated within a Kitaev phase estimation algorithm (PEA). We consider superconducting fluxonium-qubit sensors, which are modelled with relaxation and dephasing noise. Using a Bayesian update procedure, we evaluate the estimation performance and compare the GHZ and Dicke sensors in terms of sensitivity, dynamical range, and information gain. GHZ probes achieve the highest local sensitivity, while Dicke probes maintain comparable sensitivity over a substantially wider bias interval and exhibit improved tolerance to bias errors and edge effects in PEA sequence. Our results demonstrate a trade-off between local peak sensitivity and the achievable dynamical range and robustness under noise.
Recently, a DC magnetometry protocol utilizing NNN-spin-ensemble superradiance was proposed. This method physically amplifies the acquired signal, suppressing estimation errors from measurement noise and achieving O(1/N)\mathcal{O}(1/N)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 O(1/N)\mathcal{O}(1/N)O(1/N) to O(1/N)\mathcal{O}(1/\sqrt{N})O(1/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-NNN 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 N\sqrt{N}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.
Entangled states can potentially be used to outperform the standard quantum limit by which every classical sensor is bounded. However, entangled states are very susceptible to decoherence, and so it is not clear whether one can really create a superior sensor to classical technology via a quantum strategy which is subject to the effect of realistic noise. This paper presents an investigation of how a quantum sensor composed of many spins is affected by independent dephasing. We adopt general noise models including non-Markovian effects, and in these noise models the performance of the sensor depends crucially on the exposure time of the sensor to the field. We have found that, by choosing an appropriate exposure time within the non-Markovian time region, an entangled sensor does actually beat the standard quantum limit. Since independent dephasing is one of the most typical sources of noise in many systems, our results suggest a practical and scalable approach to beating the standard quantum limit.
Quantum sensing leverages non-classical resources to enhance precision. In particular, Greenberger-Horne-Zeilinger (GHZ) states can, in principle, attain the Heisenberg limit that surpasses the standard quantum limit. While many studies have examined how open-system noise-typically modeled with Lindblad master equations-degrades GHZ-based metrology, coherent control imperfections during state preparation and readout have received less attention. Here, we analyze the effect of detuning between actual and nominal spin frequencies in a GHZ-state preparation scheme employing a frequency selective pulse. We show that detuning induces coherent, systematic error that prevents GHZ sensing from reaching the Heisenberg limit. To mitigate this effect, we design a composite-pulse protocol that compensates for detuning-induced errors and improves the sensitivity under the effect of coherent error.
Entanglement has been proposed as a means to improve the sensitivity of sensing weak signals. While the degree of this quantum advantage is well understood in noiseless settings, the situation is more complex under realistic conditions, where the system is subject to decoherence. In this case, the enhancement depends on the specific noise characteristics. Previous treatments of colored noise typically assume that the noise is uncorrelated between successive experiments. Here, we consider the scenario in which the noise exhibits correlations across multiple shots. We derive a simple fundamental limit to the sensitivity based on the fact that the sensitivity cannot be better than the signal-to-noise ratio seen by the probe. Focusing on Ramsey spectroscopy with probes affected by pure classical dephasing, we show that, for suitable spatial and temporal noise correlations, entangled probes achieve a better scaling of the sensitivity with the number of probes than separable states. This demonstrates that entanglement can provide a substantial improvement for Ramsey spectroscopy subject to correlated noise.