Entanglement-enhanced AC magnetometry in the presence of Markovian noises

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.

💡 Research Summary

The paper investigates whether entanglement can still provide a metrological advantage in the presence of parallel Markovian noise when measuring alternating‑current (AC) magnetic fields. While it is well‑known that for direct‑current (DC) field sensing the Heisenberg‑limited scaling of a Greenberger‑Horne‑Zeilinger (GHZ) state collapses to the standard quantum limit (SQL) under independent parallel dephasing (the decoherence rate scales as (L) for an (L)‑qubit GHZ state), the authors show that this conclusion does not hold for AC magnetometry when the sensor qubits are detuned from the signal frequency.

Model and Hamiltonian
Each qubit has a free Hamiltonian (H_i^0 = -\frac{\omega}{2}\sigma_i^Z) and couples to the target AC field via (\Delta H_i = -\epsilon\sigma_i^X\cos(mt)), where (\epsilon) is the unknown field amplitude, (m) the field frequency, and (\omega) the qubit transition frequency. The authors deliberately consider a large detuning (|m-\omega|/\omega\gtrsim1) and therefore retain all oscillating terms in the interaction picture, avoiding the rotating‑wave approximation.

Noise channels
Two Markovian noise models are examined:

1. Parallel dephasing: independent Lindblad operators (\mathcal{D}_X