Quantum-enhanced parameter estimation has widespread applications in many fields. An important issue is to protect the estimation precision against the noise-induced decoherence. Here we develop a general theoretical framework for improving the precision for estimating an arbitrary parameter by monitoring the noise-induced quantum trajectories (MQT) and establish its connections to the purification-based approach to quantum parameter estimation. Monitoring the noise-induced quantum trajectory can be achieved in two ways: (i) Any quantum trajectories can be monitored by directly monitoring the environment, which is experimentally challenging for realistic noises, and (ii) certain quantum trajectories can also be monitored by frequently measuring the quantum probe alone via ancilla-assisted encoding and error detection. This establishes an interesting connection between MQT and the full quantum-error-correction protocol. Application of MQT to estimate the level splitting and decoherence rate of a spin 1/2 under typical decoherence channels demonstrate that it can avoid the long-time exponential loss of the estimation precision and, in special cases, recover the Heisenberg scaling.
Quantum-enhanced parameter estimation has widespread applications in many fields. An important issue is to protect the estimation precision against the noise-induced decoherence. Here we develop a general theoretical framework for improving the precision for estimating an arbitrary parameter by monitoring the noise-induced quantum trajectories (MQT) and establish its connections to the purification-based approach to quantum parameter estimation. Monitoring the noise-induced quantum trajectory can be achieved in two ways: (i) Any quantum trajectories can be monitored by directly monitoring the environment, which is experimentally challenging for realistic noises, and (ii) certain quantum trajectories can also be monitored by frequently measuring the quantum probe alone via ancilla-assisted encoding and error detection. This establishes an interesting connection between MQT and the full quantum-error-correction protocol. Application of MQT to estimate the level splitting and decoherence rate of a spin 1/2 under typical decoherence channels demonstrate that it can avoid the long-time exponential loss of the estimation precision and, in special cases, recover the Heisenberg scaling.
Quantum continuous measurement strategies are an essential element in many modern sensing technologies, leading to potentially enhanced estimation of unknown physical parameters. In such schemes, continuous monitoring of the quantum system, which encodes the parameters of interest, gives rise to different quantum trajectories conditioned on the measurement outcomes which carry information on the parameters themselves. Importantly, different trajectories carry different amounts of information, i.e., they are more or less sensitive to the unknown parameters of interest. In this work, we propose an approach on how to systematically engineer the quantum open-system dynamics in order to increase the probability of obtaining trajectories of high sensitivity. We focus on the simplest case scenario of a single two-level system interacting with ancillas, which are in turn measured using the discretized version of continuous monitoring. We analyze the performance of our protocol and demonstrate that it may lead to a substantial enhancement of sensitivity, as quantified by the classical Fisher information, even when applied to such small system sizes, holding the promise of direct implementation in state-of-the-art experimental platforms and large, complex many-body systems.
Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises to improve the metrology performance. Our scheme can automatically alter the parameter-encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem of frequency estimation under several typical Markovian noise channels. By comparing our control-enhanced scheme with the standard scheme and the ancilla-assisted scheme, we show that our scheme performs better and can improve the estimation precision up to around one order of magnitude. Furthermore, we conduct a proof-of-principle experiment in a nuclear magnetic resonance system to verify the effectiveness of the proposed scheme. The research here is helpful for current quantum platforms to harness the power of quantum metrology in realistic noise environments.
For single-parameter sensing, Greenberger-Horne-Zeilinger (GHZ) probes achieve optimal quantum-enhanced precision across the unknown parameter range, solely relying on parameter-independent separable measurement strategies for all values of the unknown parameter. However, in the multiparameter setting, a single GHZ probe not only fails to achieve quantum advantage but also the corresponding optimal measurement becomes complex and dependent on the unknown parameters. Here, we provide a recipe for multiparameter sensing with GHZ probes using quantum error correction techniques by treating all but one unknown parameters as noise, whose effects can be corrected. This strategy restores the core advantage of single parameter GHZ-based quantum sensing, namely reaching optimally quantum-enhanced precision for all unknown parameter values while keeping the measurements separable and fixed. Specifically, given one shielded ancilla qubit per GHZ probe, our protocol extracts optimal possible precision for any probe size. While this optimal precision is shot-noise limited for a single GHZ probe, we recover the Heisenberg scaling through use of multiple complementary GHZ probes. We demonstrate the effectiveness of the protocol with Bayesian estimation.
We review some recent results regarding the use of time-continuous measurements for quantum-enhanced metrology. First, we present the underlying quantum estimation framework and elucidate the correct figures of merit to employ. We then report results from two previous works where the system of interest is an ensemble of two-level atoms (qubits) and the quantity to estimate is a magnetic field along a known direction (a frequency). In the first case, we show that, by continuously monitoring the collective spin observable transversal to the encoding Hamiltonian, we get Heisenberg scaling for the achievable precision (i.e., 1 / N for N atoms); this is obtained for an uncorrelated initial state. In the second case, we consider independent noises acting separately on each qubit and we show that the continuous monitoring of all the environmental modes responsible for the noise allows us to restore the Heisenberg scaling of the precision, given an initially entangled GHZ state.
We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement. We show that by using tools from quantum error correction this limitation can be overcome. This is demonstrated in two scenarios, including a many-body Hamiltonian with single-qubit dephasing or depolarizing noise and a single-body Hamiltonian with transversal noise. In both cases, we show that Heisenberg scaling, and hence a quadratic improvement over the classical case, can be retained. Moreover, for the case of frequency estimation we find that the inclusion of error correction allows, in certain instances, for a finite optimal interrogation time even in the asymptotic limit.
Measuring stochastic signals ("noise metrology") constitutes a central task in quantum sensing and the characterization of open quantum systems. Here we establish ultimate precision bounds for multiparameter estimation of stochastic signals encoded through Markovian Lindblad dynamics, allowing for arbitrary quantum control and noiseless ancillae. Although Markovianity enforces standard-quantum-limit scaling with sensing time T, our bounds reveal Heisenberg-type scaling in the number of dissipative channels, R: when the stochastic signal exhibits high-rank correlations across the R channels and the probe is entangled, the average variance (per parameter) scales no better than Ω(1/(TR2)). For collective k-body dissipation, R=Θ(Nk), signifying super-Heisenberg scaling with the system size N. We further show that, when the unknown parameters enter through the dissipative eigenrates, a Rapid Prepare-and-Measure (RPM) protocol that tracks many distinct quantum jumps in parallel attains these limits. In this regime, the estimation problem reduces to a multi-Poisson counting model, providing a conceptually clean route to optimal quantum noise metrology. We illustrate the breadth of the framework with applications to networked noise metrology, collective many-body dissipation, learning Pauli noise, and subdiffraction quantum imaging.