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One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this work, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies., Comment: 6 + 23 pages, 10 figures; close to the published version

Nowadays, high-quality metal oxide thin film transistors grown by solution process have the most potential to replace the traditional a-Si TFT as the next generation of transparent electronics for various applications. However, the low intrinsic carrier concentration and poor charge carrier mobility of metal oxide thin film hinder its development. In order to solve these problems, the heterojunction structure was proposed. In this study, the Indium Oxide/Indium Gallium Oxide (In2O3/IGO) heterojunction was systematically investigated, and the existence of a two-dimensional electron gas was found. There is a large accumulation of carriers at the In2O3/IGO heterojunction interface, and the Hall tests show that the In2O3/IGO heterojunction has the highest carrier concentration of 7.82 × 1012 cm−2 and a carrier mobility of 10.22 cm2V−1s−1. This research can provide a theoretical guidance for promoting the development of oxide thin film transistor technology.

The accelerated aging of China’s population will inevitably increase the burden of social retirement and significantly impact the development of financial markets, which is not conducive to sustainable social development. A proper allocation of financial assets will enable households to earn more property income and facilitate the appropriate allocation of social capital. The aging of the population is an essential factor affecting the allocation of financial assets to households. This paper examines the impact of an aging population on household financial asset allocation based on data from the 2015, 2017, and 2019 China Household Finance Surveys (CHFS). The study finds that aging significantly negatively affects household risky financial asset participation, depth of participation, and diversity. The findings remain robust after robustness tests using a two-way fixed effects model. In addition, this paper examines the mechanisms of influence from the perspectives of both risk aversion and financial literacy. In terms of mediating variables, aging increases the risk aversion of household heads, and an increase in risk aversion discourages households from investing in risky financial assets. In terms of moderating variables, the dampening effect of aging on investment in risky financial assets diminishes as financial literacy increases. In addition, empirical findings based on heterogeneity find that aging has a stronger negative impact on risky financial asset participation, depth of participation, and diversity in rural areas. Aging has a stronger negative impact on risky financial asset participation for households with children.

In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The characterization of the discrepancy is an important subject in quantum information science, which plays a key role in understanding the difference between the structures of the quantum and classical information. Here we analyze the discrepancy in terms of the Fisher information metric and present a framework that can provide analytical bounds on the difference under hierarchical quantum measurements. Specifically, we present a set of analytical bounds on the difference between the quantum and classical Fisher information metric under hierarchical p-local quantum measurements, which are measurements that can be performed collectively on at most p copies of quantum states. The results can be directly transformed to the precision limit in multi-parameter quantum metrology, which leads to characterizations of the tradeoff among the precision of different parameters. The framework also provides a coherent picture for various existing results by including them as special cases., This is a short version of arXiv:2109.05807

Although perovskite/two-dimensional (2D) materials heterojunctions have been employed to improve the optoelectronic performance of perovskite photodetectors and solar cells, effects of the intrinsic potential difference (

Heisenberg scaling characterizes the ultimate precision of parameter estimation enabled by quantum mechanics, which represents an important quantum advantage of both theoretical and technological interest. Here, we present a comprehensive and rigorous study of the attainability of strong, global notions of Heisenberg scaling (in contrast to the commonly studied local estimation based on e.g. quantum Fisher information) in the fundamental problem of quantum metrology, in noisy environments. As our first contribution, we formally define two useful notions of Heisenberg scaling in global estimation respectively based on the average estimation error and the limiting distribution of estimation error (which we highlight as a practically important figure of merit). A main result of this work is that for the standard phase damping noise, an O(n −1) noise rate is a necessary and sufficient condition for attaining global Heisenberg scaling. We first prove that O(n −1) is an upper bound on the noise rate for Heisenberg scaling to be possible, and then show by constructing a ‘robust’ estimation procedure that global Heisenberg scaling in both senses can indeed be achieved under Θ(n −1) noise. In addition, we provide a practically more friendly adaptive protocol using only an one-qubit memory, which achieves global Heisenberg scaling in terms of limiting distribution as well under O(n −1) noise.

Generally, growing phase pure CsPbBr3 single crystals is challenging, and CsPb2Br5 or Cs4PbBr6 by‐products are usually formed due to the different solubilities of CsBr and PbBr2 in the single solvent. Herein, the growth of high‐quality phase pure CsPbBr3 perovskite single crystals at room temperature by a humidity controlled solvent evaporation method is reported first. Meanwhile, the room temperature phase transition process from three dimensional (3D) cubic CsPbBr3 to two dimensional (2D) layered tetragonal CsPb2Br5 and the detailed mechanism induced by humidity are revealed. Moreover, compared with the organic–inorganic perovskite, the prepared CsPbBr3 single crystals are much more stable under high humidity, which satisfies the long‐term working conditions of X‐ray detectors. The X‐ray detectors based on CsPbBr3 single crystals show a high sensitivity and a low detection limit of 1.89 μGyair s–1, all of which meet the needs of medical diagnosis., The mixed products of CsBr and PbBr2 are rich and diverse, which is a phenomenon of people scratching their heads. In the humidity controlled low‐temperature preparation process, the mechanism of its diversity is uncovered through the transformations of products under the influence of different conditions and a valuable guidance is provided for the subsequent crystal acquisition and growth.

Quantum control can be employed in quantum metrology to improve the precision limit for the estimation of unknown parameters. The optimal control, however, typically depends on the actual values of the parameters and thus needs to be designed adaptively with the updated estimations of those parameters. Traditional methods, such as gradient ascent pulse engineering (GRAPE), need to be rerun for each new set of parameters encountered, making the optimization costly, especially when many parameters are involved. Here we study the generalizability of optimal control, namely, optimal controls that can be systematically updated across a range of parameters with minimal cost. In cases where control channels can completely reverse the shift in the Hamiltonian due to a change in parameters, we provide an analytical method which efficiently generates optimal controls for any parameter starting from an initial optimal control found by either GRAPE or reinforcement learning. When the control channels are restricted, the analytical scheme is invalid, but reinforcement learning still retains a level of generalizability, albeit in a narrower range. In cases where the shift in the Hamiltonian is impossible to decompose to available control channels, no generalizability is found for either the reinforcement learning or the analytical scheme. We argue that the generalization of reinforcement learning is through a mechanism similar to the analytical scheme. Our results provide insights into when and how the optimal control in multiparameter quantum metrology can be generalized, thereby facilitating efficient implementation of optimal quantum estimation of multiple parameters, particularly for an ensemble of systems with ranges of parameters., 13 pages, 12 figures

Quantum discrimination and estimation are pivotal for many quantum technologies, and their performance depends on the optimal choice of probe state and measurement. Here we show that their performance can be further improved by suitably tailoring the pulses that make up the interferometer. Developing an optimal control framework and applying it to the discrimination and estimation of a magnetic field in the presence of noise, we find an increase in the overall achievable state distinguishability. Moreover, the maximum distinguishability can be stabilized for times that are more than an order of magnitude longer than the decoherence time., 9 pages, 5 figures

Experiments demonstrate very high precisions achieved simultaneously for multiple parameters with noncommuting generators., Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.

The quantum speed limit is a fundamental concept in quantum mechanics, which aims at finding the minimum time scale or the maximum dynamical speed for some fixed targets. In a large number of studies in this field, the construction of valid bounds for the evolution time is always the core mission, yet the physics behind it and some fundamental questions like which states can really fulfill the target, are ignored. Understanding the physics behind the bounds is at least as important as constructing attainable bounds. Here we provide an operational approach for the definition of the quantum speed limit, which utilizes the set of states that can fulfill the target to define the speed limit. Its performances in various scenarios have been investigated. For time-independent Hamiltonians, it is inverse-proportional to the difference between the highest and lowest energies. The fact that its attainability does not require a zero ground-state energy suggests it can be used as an indicator of quantum phase transitions. For time-dependent Hamiltonians, it is shown that contrary to the results given by existing bounds, the true speed limit should be independent of the time. Moreover, in the case of spontaneous emission, we find a counterintuitive phenomenon that a lousy purity can benefit the reduction of the quantum speed limit., 9+9 pages, 10 figures

In this paper, we continue our investigation on controlling the state of a quantum harmonic oscillator, by coupling it to a reservoir composed of a sequence of qubits. Specifically, we show that sending qubits separable from each other but initialised at different states in pairs can stabilise the oscillator at squeezed states. However, only if entanglement is allowed in the reservoir qubit can we stabilise the oscillator at a wider set of squeezed states. This thus provides a proof for the necessity of involving entanglement in the reservoir qubits input to the oscillator, as regard to the stabilisation of quantum states in the proposed system setting. On the other hand, this system setup can be in turn used to estimate the coupling strength between the oscillator and reservoir qubits. We further demonstrate that entanglement in the reservoir input qubits contributes to the corresponding quantum Fisher information. From this point of view, entanglement is proved to play an indispensable role in the improvement of estimation precision in quantum metrology., Accepted by Conference on Decision and Control, 2019

Quantum metrology can achieve far better precision than classical metrology, and is one of the most important applications of quantum technologies in the real world. To attain the highest precision promised by quantum metrology, all steps of the schemes need to be optimized, which include the state preparation, parametrization, and measurement. Here the recent progresses on the optimization of these steps, which are essential for the identification and achievement of the ultimate precision limit in quantum metrology, are reviewed. It is hoped this provides a useful reference for the researchers in quantum metrology and related fields., 21 pages, 7 figures

Generally, growing phase pure CsPbBr3 single crystals is challenging, and CsPb2Br5 or Cs4PbBr6 by‐products are usually formed due to the different solubilities of CsBr and PbBr2 in the single solvent. Herein, the growth of high‐quality phase pure CsPbBr3 perovskite single crystals at room temperature by a humidity controlled solvent evaporation method is reported first. Meanwhile, the room temperature phase transition process from three dimensional (3D) cubic CsPbBr3 to two dimensional (2D) layered tetragonal CsPb2Br5 and the detailed mechanism induced by humidity are revealed. Moreover, compared with the organic–inorganic perovskite, the prepared CsPbBr3 single crystals are much more stable under high humidity, which satisfies the long‐term working conditions of X‐ray detectors. The X‐ray detectors based on CsPbBr3 single crystals show a high sensitivity and a low detection limit of 1.89 μGyair s–1, all of which meet the needs of medical diagnosis.

Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\left| 0 \right\rangle + \left| N \right\rangle } \right)/\sqrt 2$$\end{document}0+N∕2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼N−0.94. A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications., Reaching a quantum advantage in metrology usually requires hard-to-prepare two-mode entangled states such as NOON states. Here, instead, the authors demonstrate single-mode phase estimation using Fock states superpositions in a superconducting qubit-oscillator system.

We study the joint estimation of multiple Rabi frequencies in a multilevel system. By analytically identifying the optimal probe state and the optimal measurement, we obtain the highest precision limit for the joint estimation of multiple Rabi frequencies. We show that the joint estimation does not always outperform the separate estimation. In different regimes the joint estimation can either outperform or underperform the separate estimation. We further show that if additional adaptive quantum controls are allowed then the advantage of the joint estimation over the separate estimation can be reestablished.

The advantage of quantum metrology has been experimentally demonstrated for phase estimations where the dynamics are commuting. General noncommuting dynamics, however, can have distinct features. For example, the direct sequential scheme, which can achieve the Heisenberg scaling for the phase estimation under commuting dynamics, can have even worse performances than the classical scheme when the dynamics are noncommuting. Here we realize a scalable optimally controlled sequential scheme, which can achieve the Heisenberg precision under general noncommuting dynamics. We also present an intuitive geometrical framework for the controlled scheme and identify sweet spots in time at which the optimal controls used in the scheme can be prefixed without adaptation, which simplifies the experimental protocols significantly. We successfully implement the scheme up to eight controls in an optical platform and demonstrate a precision near the Heisenberg limit. Our work opens the avenue for harvesting the power of quantum control in quantum metrology, and provides a control-enhanced recipe to achieve the Heisenberg precision under general noncommuting dynamics.

Measurement and estimation of parameters are essential for science and engineering, where one of the main quests is to find systematic schemes that can achieve high precision. While conventional schemes for quantum parameter estimation focus on the optimization of the probe states and measurements, it has been recently realized that control during the evolution can significantly improve the precision. The identification of optimal controls, however, is often computationally demanding, as typically the optimal controls depend on the value of the parameter which then needs to be re-calculated after the update of the estimation in each iteration. Here we show that reinforcement learning provides an efficient way to identify the controls that can be employed to improve the precision. We also demonstrate that reinforcement learning is highly generalizable, namely the neural network trained under one particular value of the parameter can work for different values within a broad range. These desired features make reinforcement learning an efficient alternative to conventional optimal quantum control methods., Comment: 7+7 pages, 6+3 figures

A target whispering-gallery-mode microresonator (WGMM) directly coupled to a waveguide with an auxiliary side-coupled WGMM is proposed to deterministically extract both the resonant and non-resonant single incident photons from a waveguide. Based on the single-photon Raman interaction (SPRINT) between an Λ-type three-level atom and the target WGMM, a full quantum theory in real space is adopted to calculate the extraction efficiencies at the single-photon level. The results show that the extraction efficiencies can be significantly improved by appropriately tuning the frequencies of the auxiliary WGMM and the coupling strength between the two WGMMs, even when the atom and WGMMs have dissipations. Since mode redistribution is only externally imposed on the auxiliary WGMM, the population and phase of the atom are not directly affected. The nonlocal control, which ensures that the SPRINT takes place, results in high extraction efficiencies. We also find that the transmission probabilities of both the resonant and non-resonant incident photons can be controlled in a range from 0 to 100%, so that the proposed double-WGMM system has the potential to be used as a single-photon switch.

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cram\'{e}r-Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part., Comment: ~70 pages, close to published version, open access

The characteristics of ferroelectric capacitors with poly(vinylidene fluoride-trifluoroethlene) (P(VDF-TrFE)) films have been studied at different structures of cell electrodes. It is suggested that the effect of electrode structures could induce changes of performance. Remarkably, cells with line electrodes display a better polarization and fatigue resistance than those with flat electrodes. For P(VDF-TrFE) ultrathin films with different electrode structures, the models of charge compensation mechanism for depolarization field and domain fatigue decomposition are used to explain the effect of electrode structure. Furthermore, the driving voltage based on normal speed-functionality is designed, and the testing results show that the line electrode structure could induce a robust switching, which is determined by the free charges concentration in active layer. These findings provide an effective route to design the optimum structure for a ferroelectric capacitor based on P(VDF-TrFE) copolymer ultrathin film.

Most studies in multiparameter estimation assume the dynamics is fixed and focus on identifying the optimal probe state and the optimal measurements. In practice, however, controls are usually available to alter the dynamics, which provides another degree of freedom. In this paper we employ optimal control methods, particularly the gradient ascent pulse engineering (GRAPE), to design optimal controls for the improvement of the precision limit in multiparameter estimation. We show that the controlled schemes not only capable to provide a higher precision limit, but also have a higher stability to the inaccuracy of the time point performing the measurements. This high time stability will benefit the practical metrology where it is hard to perform the measurement at a very accurate time point due to the response time of the measurement apparatus., 11 pages, 2 figures, PRA published version

We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be directly obtained from the underlying dynamics. Examples are then provided to demonstrate the usefulness of the maximal quantum Fisher information matrix by deriving various tradeoff relations in multi-parameter quantum estimation and obtaining the bounds for the scalings of the precision limit., Comment: 6 pages

We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite systems that identify the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling $m$-locality, we show that the observed joint probabilities in any nonsignaling $m$-local realistic models should satisfy the $(m-1)$-th Bell-type inequality. When $m=2$ the corresponding inequality reduces to the one shown in [Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when $m=n$ the corresponding inequality is just Hardy's inequality whose violation indicates standard multipartite nonlocality. Furthermore, several examples are provided to demonstrate their hierarchy of multipartite nonlocality., 6 pages

A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, 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 on the precision limit of quantum parameter estimation. We show that by exploring the additional degree of freedom offered by the controls 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 to the standard scheme where the precision limit is always bounded by the coherent time., 15 pages, 9 figures, PRA published version

Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find out the highest achievable precision with given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter we show that the sequential feedback scheme has a 3-fold improvement over the parallel scheme for Hamiltonian parameter estimations on 2-dimensional systems, and an order of $O(d+1)$ improvement for Hamiltonian parameter estimation on $d-$dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field., 11 pages. Accepted by Phys. Rev. Lett

International audience; Here we study the optimum efficiency of the excitation of maximum quantum (MaxQ) coherence using analytical and numerical methods based on optimal control theory. The theoretical limit of the achievable MaxQ amplitude and the minimum time to achieve this limit are explored for a set of model systems consisting of up to five coupled spins. In addition to arbitrary pulse shapes, two simple pulse sequence families of practical interest are considered in the optimizations. Compared to conventional approaches, substantial gains were found both in terms of the achieved MaxQ amplitude and in pulse sequence durations. For a model system, theoretically predicted gains of a factor of three compared to the conventional pulse sequence were experimentally demonstrated. Motivated by the numerical results, also two novel analytical transfer schemes were found: Compared to conventional approaches based on non-selective pulses and delays, double-quantum coherence in two-spin systems can be created twice as fast using isotropic mixing and hard spin-selective pulses. Also it is proved that in a chain of three weakly coupled spins with the same coupling constants, triple-quantum coherence can be created in a time-optimal fashion using so-called geodesic pulses.

The fidelity function of quantum states have been widely used in quantum information science and frequently arises in the quantification of optimal performances for the estimation and distinguish of quantum states. A fidelity function on quantum channel is expected to have same wide applications in quantum information science. In this paper we propose a fidelity function on quantum channels and show that various distance measures on quantum channels can be obtained from this fidelity function, for example the Bures angle and the Bures distance can be extended to quantum channels via this fidelity function. We then show that the distances between quantum channels lead naturally to a new Fisher information which quantifies the ultimate precision limit in quantum metrology, the ultimate precision limit can thus be seen as a manifestation of the distances between quantum channels. We also show that the fidelity on quantum channels provides a unified framework for perfect quantum channel discrimination and quantum metrology, in particular we show that the minimum number of uses needed for perfect channel discrimination is exactly the counterpart of the precision limit in quantum metrology, and various useful lower bounds for the minimum number of uses needed for perfect channel discrimination can be obtained via this connection., 15 pages. Comments are particularly welcome

Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.