Quantum optimal control (QOC) schemes can be employed to enhance the sensitivity of quantum metrology (QM) protocols undergoing Markovian noise, which can limit their precision to a standard quantum limit (SQL)-like scaling. In this paper, we propose a QOC scheme for QM that leverages entanglement and optimized coupling interactions with an ancillary system to provide enhanced metrological performance under general Markovian dynamics. We perform a comparative analysis of our entanglement-enhanced scheme against the unentangled scheme conventionally employed in QOC-enabled QM for varying evolution times and decoherence levels, revealing that the entanglement-enhanced scheme enables significantly better noise performance, even when a noisy ancilla is employed. We further extend our investigation to time-inhomogeneous noise models, specifically focusing on a noisy frequency estimation scenario within a spin-boson bath, and evaluate the protocol's performance under completely dissipative and dephasing dynamics. Our findings indicate that, in certain situations, schemes employing coherent control of a single particle are severely limited. In such cases, employing the entanglement-enhanced scheme can provide improved performance.
Quantum optimal control (QOC) schemes can be employed to enhance the sensitivity of quantum metrology (QM) protocols undergoing Markovian noise, which can limit their precision to a standard quantum limit (SQL)-like scaling. In this paper, we propose a QOC scheme for QM that leverages entanglement and optimized coupling interactions with an ancillary system to provide enhanced metrological performance under general Markovian dynamics. We perform a comparative analysis of our entanglement-enhanced scheme against the unentangled scheme conventionally employed in QOC-enabled QM for varying evolution times and decoherence levels, revealing that the entanglement-enhanced scheme enables significantly better noise performance, even when a noisy ancilla is employed. We further extend our investigation to time-inhomogeneous noise models, specifically focusing on a noisy frequency estimation scenario within a spin-boson bath, and evaluate the protocol's performance under completely dissipative and dephasing dynamics. Our findings indicate that, in certain situations, schemes employing coherent control of a single particle are severely limited. In such cases, employing the entanglement-enhanced scheme can provide improved performance.
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.
Quantum metrology promises unprecedented precision of parameter estimation, but it is often vulnerable to noise. While significant efforts have been devoted to improving the metrology performance in Markovian environments, practical control schemes specifically designed for non-Markovian noises are much less investigated. Here, we propose two control-enhanced quantum metrology schemes that are suitable for tackling general non-Markovian noises described by noise channels or noise spectra. We conduct experiments to verify the efficacy of these schemes on a nuclear magnetic resonance system. The experimental results involving multiqubit probes show that the parameter estimation precision can be greatly improved, significantly surpassing the standard quantum limit, with our schemes. At present, non-Markovian noises are widely encountered on diverse quantum devices, the proposed schemes are relevant for realistic metrology applications on these platforms. Quantum metrology, a powerful paradigm for surpassing classical measurement precision, has been extensively studied for Markovian noise, while most practical physical processes obey non-Markovian dynamics. In this paper, the authors propose control-enhanced quantum metrology schemes to counteract non-Markovian noise and experimentally verify their efficacy.
This thesis explores various protocols which can be applied to quantum metrology, such that precision of the measurement can beat the best classical approaches. We first demonstrate that ancilla-assisted schemes can improve phase estimation in the presence of noise, and we propose an experiment to demonstrate these effects. Given that the use of ancillae helps, it is no surprise that there are noisy channels for which the optimal strategy may depend on the noise level. We show that there is a non-trivial crossover between the ancilla-assisted strategy and the parallel-entangled strategy for Pauli noise channels and the amplitude damping channel. We see that under certain circumstances, the environment cannot access the parameter of interest. We then integrated techniques from quantum communication, to derive a general framework that renders quantum metrology protocols into cryptographic ones. Here the protocol is unconditionally secure if the trusted parties wish only to achieve the standard quantum limit. If Heisenberg-limited precision is to be achieved, they sacrifice some security, where adversaries can access information, but only at the risk of getting caught at it (cheat-sensitivity). In many scenarios, the quantum Fisher information is achieved for only one value of the phase. In a particular phase estimation scheme that measures the parity at the output of a Mach-Zehnder interferometer where the input is a two-mode squeezed vacuum, this problem is particularly imminent. We apply an adaptive technique to resolve this issue, showing that one can achieve precisions substantially below the shot noise limit. The key to a quadratically enhanced improvement in quantum metrology is entanglement. Finally, we demonstrate in a photonic system how high-dimensional entanglement can be certified, and provide an alternate interpretation of entanglement from an information-theoretic perspective.
We establish general limits on how precise a parameter, e.g. frequency or the strength of a magnetic field, can be estimated with the aid of full and fast quantum control. We consider uncorrelated noisy evolutions of N qubits and show that fast control allows to fully restore the Heisenberg scaling (~1/N^2) for all rank-one Pauli noise except dephasing. For all other types of noise the asymptotic quantum enhancement is unavoidably limited to a constant-factor improvement over the standard quantum limit (~1/N) even when allowing for the full power of fast control. The latter holds both in the single-shot and infinitely-many repetitions scenarios. However, even in this case allowing for fast quantum control helps to increase the improvement factor. Furthermore, for frequency estimation with finite resource we show how a parallel scheme utilizing any fixed number of entangled qubits but no fast quantum control can be outperformed by a simple, easily implementable, sequential scheme which only requires entanglement between one sensing and one auxiliary qubit.
Quantum effects in metrology can in principle enhance measurement precision from the so-called standard quantum limit to the Heisenberg limit. Further advancements in quantum metrology largely rely on innovative metrology protocols that can avoid a number of known obstacles, including the challenge of preparing entangled states with sufficient fidelity, the readout noise in measuring highly entangled states, and no-go theorems for quantum metrology under noisy environments. In this Letter, exploiting some peculiar but experimentally feasible dynamical features of a collection of spins with all-to-all time-periodic interactions, we propose a metrology protocol that can circumvent all three mentioned obstacles and yet still make good use of time as a resource for metrology. Specifically, by mapping the dynamics of such a periodically driven spin system to that of a paradigm of quantum chaos but tuned to some high-order quantum resonance, it is shown that a simple SU(2) coherent state can, after evolving to highly entangled states in the ensuing dynamics, be dynamically brought back to the same initial coherent state. The associated quantum Fisher information is found to exhibit quadratic scaling with both the number of spins and the duration of the metrology protocol. The achieved Heisenberg scaling can also largely survive in the presence of Markovian noise. Representing a previously unknown strategy for quantum metrology, the protocol proposed here can be tested on available experimental platforms.
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to design schemes that achieve the highest precision with the given resources. Standard models of quantum metrology usually assume that the dynamics is fixed and that the highest precision is achieved by preparing the optimal probe states and performing optimal measurements. However, in many practical experimental settings, additional controls are usually available to alter the dynamics. Here we propose to use optimal control methods for further improvement of the precision limit of quantum parameter estimation. We show that, by exploring the additional degree of freedom offered by the controls, a higher-precision limit can be achieved. In particular, we show that the precision limit under the controlled schemes can go beyond the constraints put by the coherent time, which is in contrast with the standard scheme where the precision limit is always bounded by the coherent time.