The typical bound on parameter estimation, known as the standard quantum limit (SQL), can be surpassed by exploiting quantum resources such as entanglement. To estimate the magnetic probe field, we propose a quantum sensor based on a variable-range many-body quantum spin chain with a moderate transverse magnetic field. We report the threefold benefits of employing a long-range system as a quantum sensor. First, sensors with quasi-long-range interactions can always beat the SQL for all values of the coordination number, while a sensor with long-range interactions does not have this ubiquitous quantum advantage. Second, a long-range Hamiltonian outperforms a nearest-neighbor (NN) Hamiltonian in terms of both estimating precision and system-size scaling. Finally, we observe that the system with long-range interactions can go below the SQL in the presence of a high temperature of the initial state, while sensors having NN interactions cannot. Furthermore, a sensor based on the long-range Ising Hamiltonian proves to be robust against impurities in the magnetic field and when the time-inhomogeneous dephasing noise acts during interaction of the probe with the system.
The typical bound on parameter estimation, known as the standard quantum limit (SQL), can be surpassed by exploiting quantum resources such as entanglement. To estimate the magnetic probe field, we propose a quantum sensor based on a variable-range many-body quantum spin chain with a moderate transverse magnetic field. We report the threefold benefits of employing a long-range system as a quantum sensor. First, sensors with quasi-long-range interactions can always beat the SQL for all values of the coordination number, while a sensor with long-range interactions does not have this ubiquitous quantum advantage. Second, a long-range Hamiltonian outperforms a nearest-neighbor (NN) Hamiltonian in terms of both estimating precision and system-size scaling. Finally, we observe that the system with long-range interactions can go below the SQL in the presence of a high temperature of the initial state, while sensors having NN interactions cannot. Furthermore, a sensor based on the long-range Ising Hamiltonian proves to be robust against impurities in the magnetic field and when the time-inhomogeneous dephasing noise acts during interaction of the probe with the system.
Recent breakthroughs in quantum technology pave the way for extensive utilization of higher-dimensional quantum systems, which outperform their qubit counterparts in terms of capabilities and versatility. We present a framework for accurately predicting weak external magnetic fields using a higher-dimensional many-body quantum probe. We demonstrate that dimension serves as a valuable resource for quantum sensing when a transverse spin-s Ising chain interacts locally with a magnetic field whose strength has to be determined. We observe the distinct performance of sensors for spin chains with half-integer and integer spins. Furthermore, we highlight that the time duration appropriate for quantum-enhanced sensing increases with the increase of dimension. Additionally, we observe that, in addition to nearest-neighbor interactions, incorporating interactions between the next nearest-neighbor sites increases sensing precision, particularly for spin chains with integer spins. We also prove the dimensional-dependence of the bound on quantum Fisher information which provides the limit on the precision in estimating parameters.
Quantum metrology is the use of genuinely quantum properties such as entanglement as a resource to outperform classical sensing strategies. Typically, entanglement is created by implementing gate operations or inducing many-body interactions. However, existing sensing schemes with these approaches require accurate control of the probe system such as switching on and off the interaction among qubits, which can be challenging for practical applications. Here, we propose an entanglement-enhanced sensing scheme with an always-on nearest-neighbor interaction between qubits. We adopt the transverse field Ising chain as the probe system, making use of the so-called quantum domino dynamics for the generation of the entangled states. In addition to the advantage that our scheme can be implemented without controlling the interactions, it only requires initialization of the system, projective measurements on a single qubit, and control of the uniform magnetic fields. We can achieve an improved sensitivity beyond the standard quantum limit even under the effect of realistic decoherence.
Long-range (LR) quantum spin systems offer promising advantages for quantum information processing and sensing. Here, we investigate parameter estimation in an long-range XX spin model coupled to a reservoir, which gives rise to an effective long-range RT-symmetric non-Hermitian iXY Hamiltonian. The interactions extend up to a tunable coordination range and decay algebraically with distance, enabling a direct comparison between long-range and short-range (SR) regimes. Focusing on the estimation of the transverse magnetic field and anisotropy parameter, we initialize the system in a fully polarized state and analyze the resulting dynamical quantum Fisher information (QFI). We show that, with suitable tuning of the system parameters, both the time and system-size scaling of the QFI are enhanced in the LR regime relative to their SR counterparts. Moreover, the non-Hermitian LR model can exhibit superior dynamical QFI compared with the corresponding Hermitian model, demonstrating a genuine metrological advantage induced by the interplay of long-range interactions and non-Hermitian effects. In contrast, we establish a no-go result at the critical magnetic field: when the probe is prepared in the lowest-energy eigenstate, the QFI scaling remains identical for the Hermitian and non-Hermitian cases.
Quantum sensors outperform their classical counterparts in their estimation precision, given the same amount of resources. So far, quantum-enhanced sensitivity has been achieved by exploiting the superposition principle. This enhancement has been obtained for particular forms of entangled states, adaptive measurement basis change, critical many-body systems, and steady state of periodically driven systems. Here, we introduce a different approach to obtain quantum-enhanced sensitivity in a many-body probe through utilizing the nature of quantum measurement and its subsequent wave function collapse without demanding prior entanglement. Our protocol consists of a sequence of local measurements, without reinitialization, performed regularly during the evolution of a many-body probe. As the number of sequences increases, the sensing precision is enhanced beyond the standard limit, reaching the Heisenberg bound asymptotically. The benefits of the protocol are multifold as it uses a product initial state and avoids complex initialization (e.g., prior entangled states or critical ground states) and allows for remote quantum sensing.
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.
In this paper, we focus on the magnetic field sensing subject to a correlated noise. We use a ring spin chain with only the nearest neighbor interactions as our probe to estimate both the intensity B and the direction θ of the magnetic field when the probe reaches its steady state. We numerically calculate the quantum Fisher information (QFI) to characterize the estimation precision. On the one hand, for estimating B, we find that the coupling between spins in the probe plays an important role in the precision, and the largest value of the QFI can be achieved when θ = π/2 together with an optimal coupling. Moreover, for any direction, the precision scaling can be better than the Heisenberg-limit (HL) with a proper coupling. On the other hand, for estimating θ, we find that our probe can perform a high precision detection for θ ~ π/2, with the QFI much larger than that for any other directions, especially when the coupling is tuned to the optimal value. And we find that the precision scaling for θ ~ π/2 can be better than the HL, but for other directions, the precision scaling is only limited to the standard quantum limit (SQL). Due to the computational complexity we restrict the number of spins in the probe to 60.