G. Mauro D'Ariano, Paoloplacido Lo Presti, Matteo G. A. Paris
We show how entanglement can be used to improve the estimation of an unknown transformation. Using entanglement is always of benefit, in improving either the precision or the stability of the measurement. Examples relevant for applications are illustrated, for either qubits and continuous variables
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Squeezing of quantum fluctuations by means of entanglement is a well recognized goal in the field of quantum information science and precision measurements. In particular, squeezing the fluctuations via entanglement between two-level atoms can improve the precision of sensing, clocks, metrology, and spectroscopy. Here, we demonstrate 3.4 dB of metrologically relevant squeezing and entanglement for ~ 10^5 cold cesium atoms via a quantum nondemolition (QND) measurement on the atom clock levels. We show that there is an optimal degree of decoherence induced by the quantum measurement which maximi…
We show that the general Heisenberg Hamiltonian with non-uniform couplings can be characterised by mapping the entanglement it generates as a function of time. Identification of the Hamiltonian in this way is possible as the coefficients of each operator control the oscillation frequencies of the entanglement function. The number of measurements required to achieve a given precision in the Hamiltonian parameters is determined and an efficient measurement strategy designed. We derive the relationship between the number of measurements, the resulting precision and the ultimate discrete error pro…
It is widely accepted that quantum entanglement between otherwise independent sensors can yield a measurement precision beyond that achievable when the same resources are employed without entanglement \cite{Helstrom1969, Holevo1973a, Caves1980a, Caves1981, Wootters1981, Yurke1986, Wu1986, Xiao1987, Slusher1987, Shapiro1989, Wineland1992, Polzik1992, Kitagawa1993, Braunstein1994, Wineland1994, Sanders1995, Bollinger1996, Ou1997, Dowling1998,Soerensen1998, Brif1999, Childs2000, Fleischhauer2000, Meyer2001, Geremia2003, Giovannetti2004, Kok2004, Leibfried2004, Leibfried2005, Giovannetti2006, Naga…
We present several entanglement criteria in terms of the quantum Fisher information that help to relate various forms of multipartite entanglement to the sensitivity of phase estimation. We show that genuine multipartite entanglement is necessary to reach the maximum sensitivity in some very general metrological tasks using a two-arm linear interferometer. We also show that it is needed to reach the maximum average sensitivity in a certain combination of such metrological tasks.
Nonlinear interactions are recognized as potential resources for quantum metrology, facilitating parameter estimation precisions that scale as the exponential Heisenberg limit of $2^{-N}$. We explore such nonlinearity and propose an associated quantum measurement scenario based on the nonlinear interaction of $N$-probe entanglement generating form. This scenario provides an enhanced precision scaling of $D^{-N}/(N-1)!$ with $D > 2$ a tunable parameter. In addition, it can be readily implemented in a variety of experimental platforms and applied to measurements of a wide range of quantities, in…
We show why and when entanglement is needed for quantum-enhanced precision measurements, and which type of entanglement is useful. We give a simple, intuitive construction that shows how entanglement transforms parallel estimation strategies into sequential ones of same precision. We employ this argument to generalize conventional quantum metrology, to identify a class of noise whose effects can be easily managed, and to treat the case of indistinguishable probes (such as interferometry with light).
Entanglement-Constrained Quantum Metrology: Rapid Low-Entanglement Gains, Tapered High-Level Growth
该研究探讨了在纠缠受限条件下，通过优化量子 Fisher 信息实现参数估计的精度提升，发现低纠缠区域的快速增益和高阶纠缠下的渐进改善。
We have investigated high-precision measurements, beyond the standard quantum limit, utilizing non-classical states. Although entanglement has been considered a resource for achieving the Heisenberg limit in measurements, we show that any advantage expected from using entanglement is dependent on the measurement in question. We investigate several measurement scenarios and illustrate the role of entanglement as a resource for quantum high-precision measurement. In particular, we demonstrate that there is a regime wherein entanglement not only does not help, but prevents the achievement of the …
Optimal quantum precision in noise estimation: Is entanglement necessary?
研究探讨了在估计向量编码过程中噪声参数时，最优探测器是否需要纠缠，发现当噪声强度增加时，最优探测器的纠缠度呈现阶梯状变化，且在高噪声情况下全产品态是最优选择。
We propose an approach for collective enhancement of precision for remotely located optical lattice clocks and a way of generation of the Einstein-Podolsky-Rosen state of remote clocks. Close to Heisenberg scaling of the clock precision with the number of clocks M can be achieved even for an optical channel connecting clocks with substantial losses. This scenario utilizes a collective quantum nondemolition measurement on clocks with parallel Bloch vectors for enhanced measurement precision. We provide an optimal network solution for distant clocks as well as for clocks positioned in close prox…
Uncertainty relations between quantum Fisher information and entanglement monotones
本文研究了量子鱼尔信息与纠缠单调量之间的关系，通过引入不确定性关系，从量子鱼尔信息矩阵元素下界纠缠单调量，并展示了高维纠缠在多参数估计中的重要性。
The concepts of separability, entanglement, spin-squeezing and Heisenberg limit are central in the theory of quantum enhanced metrology. In the current literature, these are well established only in the case of linear interferometers operating with input quantum states of a known fixed number of particles. This manuscript generalizes these concepts and extends the quantum phase estimation theory by taking into account classical and quantum fluctuations of the particle number. Our analysis concerns most of the current experiments on precision measurements where the number of particles is known …
Quantum metrology exploits quantum resources and strategies to improve measurement precision of unknown parameters. One crucial issue is how to prepare a quantum entangled state suitable for high-precision measurement beyond the standard quantum limit. Here, we propose a scheme to find optimal pulse sequence to accelerate the one-axis twisting dynamics for entanglement generation with the aid of deep reinforcement learning (DRL). We consider the pulse train as a sequence of $π/2$ pulses along one axis or two orthogonal axes, and the operation is determined by maximizing the quantum Fisher info…
We analyze the role of entanglement among probes and with external ancillas in quantum metrology. In the absence of noise, it is known that unentangled sequential strategies can achieve the same Heisenberg scaling of entangled strategies and that external ancillas are useless. This changes in the presence of noise: here we prove that entangled strategies can have higher precision than unentangled ones and that the addition of passive external ancillas can also increase the precision. We analyze some specific noise models and use the results to conjecture a general hierarchy for quantum metrolo…
Matters Arising: Distributed quantum sensing with mode-entangled spin-squeezed atomic states
本文是对Malia等人2022年发表于《Nature》的分布式量子传感研究的商榷，指出其声称的四节点时钟网络纠缠精度比量子投影噪声极限高11.6 dB的结论错误，实际结果比该极限差两个数量级以上，未实现纠缠带来的精度提升。
Entanglement free Metrology Exploiting Multimode Hong Ou Mandel Sensor Advantage
本文提出利用频率乘积态和后选择频率反相关结果，证明多模HOM计量优势源于频谱反相关而非纠缠或玻色子对称性，无需强泵浦激光，便于实际应用。
Entanglement-enhanced quantum metrology: from standard quantum limit to Heisenberg limit
本文介绍纠缠增强量子计量的原理与实验进展，说明利用多粒子纠缠可突破标准量子极限、逼近海森堡极限，还探讨了相关量子传感器的潜在应用。
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its algorithmic complexity.
We report on a two-particle matter wave interferometer realized with pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin-mixture of the two atoms and then tuning the inter-state scattering length via a Feshbach resonance. The selective change of the inter-state scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic in…
Quantum squeezing cannot beat the standard quantum limit
本文证明，在量子传感中，若以不使用纠缠的相同资源无法达到的精度为成功标准，则压缩态无法超越标准量子极限，单个压缩态单位时间精度不优于单个粒子。
We identify precision limits for the simultaneous estimation of multiple parameters in multimode interferometers. Quantum strategies to enhance the multiparameter sensitivity are based on entanglement among particles, modes or combining both. The maximum attainable sensitivity of particle-separable states defines the multiparameter shot-noise limit, which can be surpassed without mode entanglement. Further enhancements up to the multiparameter Heisenberg limit are possible by adding mode entanglement. Optimal strategies which saturate the precision bounds are provided.
Quantum neuromorphic approach to efficient sensing of gravity-induced entanglement
提出一种量子神经形态平台，通过训练量子网络感知弱纠缠，实现超越标准量子极限的纠缠测量，并显著提升引力诱导纠缠的估计精度。
Precision in estimating independent local fields: attainable bound and indispensability of genuine multiparty entanglement
本研究证明，估计局域哈密顿量的独立场强需真正多体纠缠态作为探针，并给出可达精度下界，GHZ态可达到该界，而混合态和纯乘积态无法达到。
We address the experimental determination of entanglement for systems made of a pair of polarization qubits. We exploit quantum estimation theory to derive optimal estimators, which are then implemented to achieve ultimate bound to precision. In particular, we present a set of experiments aimed at measuring the amount of entanglement for states belonging to different families of pure and mixed two-qubit two-photon states. Our scheme is based on visibility measurements of quantum correlations and achieves the ultimate precision allowed by quantum mechanics in the limit of Poissonian distributio…
Invariance under Lorentz transformations is fundamental to both the standard model and general relativity. Testing Lorentz-symmetry violation (LSV) via atomic systems attracts extensive interests in theory and experiment. Some recent proposals for testing LSV present that the effects of violation can be described as a local interaction. Further, the test precision of LSV can be enhanced via quantum entanglement and its quantum Fisher information (QFI) implicates that the test precision can asymptotically reach the Heisenberg limit. In general, the limited resolution of collective observables p…
The laws of quantum physics endow superior performance and security for information processing: quantum sensing harnesses nonclassical resources to enable measurement precision unmatched by classical sensing, whereas quantum cryptography aims to unconditionally protect the secrecy of the processed information. Here, we present the theory and experiment for entanglement-enhanced covert sensing, a paradigm that simultaneously offers high measurement precision and data integrity by concealing the probe signal in an ambient noise background so that the execution of the protocol is undetectable wit…
Quantum-Enhanced Parameter Estimation Without Entanglement
该研究通过在单个高维 qudit 上构造 Dicke 与 GHZ 态类似物，证明无需纠缠即可超越标准量子极限，并以量子 Fisher 信息刻画非经典性，显著降低量子增强参数估计的资源需求。
Clock Synchronization for Drone-Based Entanglement Quantum Key Distribution
针对无人机纠缠QKD受SWaP和移动性限制的时钟同步难题，提出融合GNSS纳秒授时与纠缠定时校正的协议，在动态自由空间信道中实现24 ps RMS同步。
Sensing and measurement tasks in severely adverse conditions such as loss, noise and dephasing can be improved by illumination with quantum states of light. Previous results have shown a modest reduction in the number of measurements necessary to achieve a given precision. Here, we compare three illumination strategies for estimating the relative phase in a noisy, lossy interferometer. When including a common phase fluctuation in the noise processes, we show that using an entangled probe achieves an advantage in parameter estimation precision that scales with the number of entangled modes. Thi…
Quantum metrology allows for a huge boost in the precision of parameters estimation. However, it seems to be extremely sensitive on the noise. Bound entangled states are states with large amount of noise what makes them unusable for almost all quantum informational tasks. Here we provide a counterintuitive example of a family of bound entangled states which can be used in quantum enhanced metrology. We show that these states give advantage as big as maximally entangled states and asymptotically reach the Heisenberg limit. Moreover, entanglement of the applied states is very weak which is refle…
Large photon-number path entanglement is an important resource for enhanced precision measurements and quantum imaging. We present a general constructive protocol to create any large photon number path-entangled state based on the conditional detection of single photons. The influence of imperfect detectors is considered and an asymptotic scaling law is derived.
Precision measurements are important across all fields of science. In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration and optical path length. Quantum entanglement enables higher precision than would otherwise be possible. We demonstrate an optical phase measurement with an entangled four photon interference visibility greater than the threshold to beat the standard quantum limit--the limit attainable without entanglement. These results open the way for new high-precision measurement applications.
We address the use of entanglement to improve the precision of generalized quantum interferometry, i.e. of binary measurements aimed to determine whether or not a perturbation has been applied by a given device. For the most relevant operations in quantum optics, we evaluate the optimal detection strategy and the ultimate bounds to the minimum detectable perturbation. Our results indicate that entanglement-assisted strategies improve the discrimination in comparison with conventional schemes. A concrete setup to approach performances of the optimal strategies is also suggested.
Entanglement preparation and signal accumulation are essential for quantum parameter estimation, which pose significant challenges to both theories and experiments. Here, we propose how to utilize chaotic dynamics in a periodically driven Bose-Josephson system for achieving a high-precision measurement beyond the standard quantum limit (SQL). Starting from an initial non-entangled state, the chaotic dynamics generates quantum entanglement and simultaneously encodes the parameter to be estimated. By using suitable chaotic dynamics, the ultimate measurement precision of the estimated parameter c…
Utilizing probabilistic entanglement between sensors in quantum networks
针对星形量子传感网络中纠缠概率生成且保真度有限的问题，本文利用量子 Fisher 信息比较协议，给出纠缠使用、存储与提纯的条件及经典传感更优的保真度阈值。
Quantum metrology is studied in the presence of quantum correlation. The quantum correlation measure based on quantum Fisher information enables us to gain a deeper insight on how quantum correlations are instrumental in setting metrological precision. Our analysis shows that not only the entanglement but also the quantum correlation plays important roles to enhance precision in quantum metrology. Even in the absence of entanglement, quantum correlation can be exploited as the resource to beat standard quantum limit and reach Heisenberg limit in metrology. Clearly unraveling the role of quantu…
A recent proposal for testing Lorentz symmetry violation (LSV) presents a formulation where the effect of violation is described as a local interaction [R. Shaniv, et al, Phys. Rev. Lett. 120, 103202 (2018)]. An entangled ion pair in a decoherence free subspace (DFS) is shown to double the signal to noise ratio (SNR) of one ion, while (even)-N/2 such DFS pairs in a collective entangled state improve SNR by N times, provided the state parity or the even/odd numbers of ions can be measured. It remains to find out, however, how such fiducial entangled states can be prepared at nonexponentially sm…
In this paper, we investigate how to reduce the number of measurement configurations needed for sufficiently precise entanglement quantification. Instead of analytical formulae, we employ artificial neural networks to predict the amount of entanglement in a quantum state based on results of collective measurements (simultaneous measurements on multiple instances of the investigated state). This approach allows us to explore the precision of entanglement quantification as a function of measurement configurations. For the purpose of our research, we consider general two-qubit states and their ne…
The goal of quantum metrology is the exploitation of quantum resources, like entanglement or quantum coherence, in the fundamental task of parameter estimation. Here we consider the question of the estimation of the Unruh temperature in the scenario of relativistic quantum metrology. Specifically, we study two distinct cases. First, a single Unruh-DeWitt detector interacting with a scalar quantum field undergoes an uniform acceleration for a finite amount of proper time, and the role of coherence in the estimation process is analyzed. After this, we consider two initially entangled detectors, …
Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise, experimental feasible measure of entanglement. Nevertheless, such measurements are limited both from experimental uncertainties and intrinsic quantum bounds. Here we present an experiment where the amount of entanglement of a family of two-qubit mixed photon states is estimated with the ultimate precision allowed by quantum mechanics.
An entanglement protocol to measure atomic parity violation at sub 0.1% precision
本文提出一种基于多离子纠缠态的协议，在钡离子中实现低于0.1%精度的原子宇称破坏测量，通过共模抑制和选择性探测，免除了11个数量级的系统误差抑制，并可扩展至大规模离子数以提高精度。
Fundamental wave features of light play an important role in the realization of superresolution for two spatially separated point sources. It has been shown that (partial) coherence, which is an inevitable feature in practical light propagation, is harmful to measurement precision thus preventing superresolution. Here we study the quantitative effect of another fundamental feature, entanglement, on the quality of superresolution and compare it with that of coherence. Both single- and two-parameter estimations are analyzed in detail. Surprisingly, contrary to coherence, it is found that superre…
Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation.
The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $F$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in qu…
Robust and Indestructible Macroscopic Entanglement
该研究考虑退相干、粒子损失、有限精度测量等现实因素，研究宏观纠缠的观测可行性并给出鲁棒宏观纠缠的操作定义，还提出更具韧性的宏观纠缠概念，通过简单例子证明其可借助一类量子态实现，为推广宏观领域量子纠缠概念开辟路径。
Quantum metrology and quantum communications are typically considered as distinct applications in the broader portfolio of quantum technologies. However, there are cases where we might want to combine the two and recent proposals have shown how this might be achieved in entanglement-based systems. Here we present an entanglement-free alternative that has advantages in terms of simplicity and practicality, requiring only individual qubits to be transmitted. We demonstrate the performance of the scheme in both the low and high data limits, showing quantum advantages both in terms of measurement …
Measurement Uncertainty in Infrared Spectroscopy with Entangled Photon Pairs
该研究针对红外波段纠缠多参数光谱测量机制不明的问题，发现了约束纠缠光子对红外光谱多参数测量精度的不确定关系，揭示了折射率与吸收系数测量精度的权衡规律，为纠缠辅助光谱的实验设计与应用提供指导。
Quantum experiments usually assume the existence of perfect, classical, reference frames, which allow for the specification of measurement settings (e.g. orientation of the Stern Gerlach magnet in spin measurements) with arbitrary precision. If the reference frames are "bounded" (i.e. quantum systems themselves, having a finite number of degrees of freedom), only limited precision can be attained. Using spin coherent states as bounded reference frames we have found their minimal size needed to violate local realism for entangled spin systems. For composite systems of spin-1/2 particles referen…
Restoring metrological quantum advantage of measurement precision in noisy scenario
本文证明在局域退相干噪声下，通过引入伊辛相互作用可恢复最大纠缠态在频率估计中的量子优势，并揭示耦合常数估计精度随初始纠缠增加而单调下降。
Error Free Quantum Target Finding: When Sequential Detection Meets High Dimensional Entanglement
本文提出利用高维贝尔态结合序贯决策规则，在有限能量下实现激光雷达目标发现与测距的渐近零误差，从而获得超越经典方法的无界量子优势。
In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum entanglement between the sensing probes and they have been shown to be optimal in the asymptotic limit in the number of probes, as long as one performs measurements on shorter and shorter time scales. Here, we present a different approach to frequency estimation, which exploits quantum coherence in the state of each sensing particle in the long time limit and …
Machine classification of quantum correlations for entanglement distribution networks
本文提出利用人工神经网络（ANN）基于纠缠交换几何中的集体测量，对纠缠分发网络中的两比特量子态关联进行资源高效的五分类，并分析了模型精确率与召回率随集体测量次数变化的函数关系。
The optimal precision of frequency measurements in the presence of decoherence is discussed. We analyze different preparations of n two level systems as well as different measurement procedures. We show that standard Ramsey spectroscopy on uncorrelated atoms and optimal measurements on maximally entangled states provide the same resolution. The best resolution is achieved using partially entangled preparations with a high degree of symmetry.
We demonstrate how quantum entanglement can be used for precision frequency measurements with trapped ions. In particular, we show how to suppress linear Zeeman shifts in optical frequency measurements by using maximally entangled states of two ions even if the individual ions do not have any field-independent transition. In addition, this technique allows for an accurate measurement of small external field frequency shifts such as the electric quadrupole shift which are important for ion clock experiments.
We show that the generation of entanglement of two heavily macroscopic mirrors with masses of up to several kilograms are feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the Standard Quantum Limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and prov…
Symmetry-protected many-body Ramsey spectroscopy: precision scaling and robustness
本文提出对称性保护的破坏性多体拉姆齐干涉测量，利用自旋猫态和匹配对称性，使测量精度接近海森堡极限，并系统分析其对噪声和实验不完美性的鲁棒性。
Deployment of Entanglement-Based QKD in Financial Infrastructure
研究基于纠缠的量子密钥分发在金融基础设施中的部署，利用偏振纠缠通过22公里光纤链路实现，全自动系统连续四个月生成安全密钥，正常运行时间达93.7%，展示了eQKD在金融基础设施中的实际集成可行性。
We consider the optimal control problem in a two-qubit system with bounded amplitude. Two cases are studied: quantum state preparation and entanglement creation. Cost functions, fidelity and concurrence, are optimized over bang-off controls for different values of the total duration, respectively. For quantum state preparation problem, three critical time points are determined with high precision, and optimal controls are obtained for different durations. A better estimation of the quantum speed limit is obtained, so is the time-optimal control. For entanglement creation problem, two critical …
We have introduced a measure of Gaussian quantum correlations based on quantum Fisher information. For bipartite Gaussian states the minimum quantum Fisher information due to local unitary evolution on one of the parties reliably quantifies quantum correlation. In quantum metrology the proposed measure becomes the tool to investigate the role of quantum orrelation in setting metrological precision. In particular, a deeper insights can be gained on how quantum correlations are instrumental to enhance metrological precision. Our analysis demonstrates that not only entanglement but also quantum c…
Entanglement-Enhanced Quantum Nano-Vibrometry
该研究通过量子纠缠提升纳米振动测量精度，实现高频率振动信号的恢复并验证量子优势。
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