Quantum Imaging and Metrology
Hwang Lee, Pieter Kok, Jonathan P. Dowling
对量子纠缠的操纵在提高陀螺仪、时钟甚至计算机等设备的性能方面具有巨大的潜力。类似的改进已经被证明用于光刻和显微镜。本文综述了量子纠缠在成像和计量学中的应用。
The manipulation of quantum entanglement has found enormous potential for improving performances of devices such as gyroscopes, clocks, and even computers. Similar improvements have been demonstrated for lithography and microscopy. We present an overview of some aspects of enhancement by quantum entanglement in imaging and metrology.
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Quantum Computing, Metrology, and Imaging
信息科学正在进入一个新的时代，其中量子力学的某些微妙之处使计算效率和通信安全性大大提高。当然，实现量子信息处理协议所需的量子系统的精确控制意味着其他科学和技术的潜在突破。我们讨论了光学系统中量子控制的最新发展及其在计量和成像中的应用。
Entangled Fock states for Robust Quantum Optical Metrology, Imaging, and Sensing
我们提出了一类路径纠缠光子Fock态，用于在存在损耗的情况下进行稳健的量子光学计量、成像和传感。我们模型的传播损耗与分束器，并推导出一个减少密度矩阵形式主义，我们研究光子损失如何影响相干性。结果表明，特定的纠缠数态，其中包含一个特殊的叠加的两个手臂的马赫-曾德尔干涉仪的光子，是弹性的环境退相干。我们证明了一个数量级更大的可见性与损失，比可能与N 00 N状态。我们还表明，检测方案的有效性与超分辨率可见性有关。
Non-classical correlations in optical beams offer the unprecedented opportunity of surpassing conventional limits of sensitivity and resolution in optical measurements and imaging, especially but not only, when a low photon flux down to the single photons are measured. We review the principles of quantum imaging and sensing techniques which exploit sub-Poissonian photon statistics and non-classical photon number correlation, presenting some state-of-the-art achievements in the field. These quantum photonics protocols have the potential to trigger major steps in many applications, such as micro…
Quantum optical technologies for metrology, sensing and imaging
在过去的20年里，明亮的纠缠光子源导致了量子光学干涉术的复兴。光干涉测量已经被用来测试量子力学的基础，并实现一些与量子纠缠相关的新想法，如量子隐形传态、量子密码学、量子光刻、量子计算逻辑门和量子精密测量。在本文中，我们重点介绍了在量子精密测量中利用量子光学纠缠来克服散粒噪声极限的新方法，例如，用于光纤陀螺仪和用于生物或化学目标的传感器。我们还讨论了如何利用这种纠缠来击败成像系统中的瑞利衍射极限，如激光雷达和光学光刻。
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problem…
Entanglement detection and quantum metrology by Stokes photon diffraction imaging
研究表明，自发散射Stokes光子的远场衍射图像可用于冷原子系综中自旋纠缠的探测和场梯度的计量。对于自旋激发数不确定性很小或最大的多体态，纠缠只是通过尖锐的衍射峰或谷的存在来证明。利用非均匀自旋进动引起的衍射峰位移来测量外场梯度矢量，这为在没有纠缠的情况下实现超出标准量子极限的精确测量提供了新的可能性。监测衍射峰的时间衰减也可以实现对囚禁冷原子气体中温度和碰撞相互作用的非破坏探测。该方法可以很容易地推广到冷分子，囚禁离子，和固态自旋系综。
Quantum Imaging and Metrology with Undetected squeezed Photons: Noise Canceling and Noise Based Imaging
提出配备零差检测和 OPO 的未探测压缩光子量子成像方案，建立超越低增益近似的理论，并通过噪声编码信息实现高信噪比、抑噪的非破坏性成像与相位测量。
Quantum metrology and its application in biology
量子精密测量提供了一种克服传感器件中的实际限制的途径。它与生物学特别相关，其中灵敏度和分辨率限制限制了基础生物物理学和医学中的应用。在这里，我们审查量子精密测量从这个生物背景下，由于其特定的相关性，生物成像，传感和刺激的光学技术为重点。我们对量子力学的理解已经在生物学中实现了重要的应用，包括使用纠缠光子的正电子发射断层成像（PET）、使用核磁共振的磁共振成像（MRI）以及使用超导量子干涉器件（SQUID）的生物磁成像。在量子精密测量中，更大范围的应用来自于不仅理解而且设计量子水平上的相干性和相关性的能力。在过去的几年里，在将这些想法应用于生物系统方面取得了相当大的进展。已经证明的能力包括提高灵敏度和分辨率，对成像伪影和技术噪声的免疫力，以及在单光子水平上对光的生物反应的表征。新的量子测量技术提供了更大的希望，提高了改进多光子显微镜和磁成像的前景，以及许多其他可能的应用。实现这一潜力将需要生物学和量子物理学研究人员的跨学科投入。在这篇评论中，我们试图沟通的量子精密测量的发展方式，是生物学家和bioprophicists访问，同时提供足够的细节，让感兴趣的读者获得坚实的理解该领域。我们进一步寻求引入量子物理学家在生物科学中的光学测量的一些核心挑战。
Entanglement-Seeded-Dual Optical Parametric Amplification: Applications to Quantum Communication, Imaging, and Metrology
光学参量放大器（OPA）的研究已经成功地描述和产生用于诸如量子精密测量和量子光刻等领域的非经典光[Agarwal等人，J. Opt. Soc. Am. B，24，2（2007）]。在本文中，我们提出了一种利用纠缠态输入的OPA方案的理论。该方案涉及两个相同的OPA，并将最大路径纠缠的N 00 N态作为种子（|2，0>+|0，2>）/sqrt{2}。受激放大导致输出态的几率幅依赖于每个模中的光子数，这与双模压缩真空有很大的不同。输出包含一族可直接应用于量子密钥分发的纠缠态。特定的输出状态允许预先创建N=4 N 00 N状态，其可以用于量子光刻，以写入亚瑞利条纹图案，以及用于量子干涉测量，以实现海森堡限制的相位测量灵敏度。
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 researcher…
Quantum metrology is an auspicious discipline of quantum information which is currently witnessing a surge of experimental breakthroughs and theoretical developments. The main goal of quantum metrology is to estimate unknown parameters as accurately as possible. By using quantum resources as probes, it is possible to attain a measurement precision that would be otherwise impossible using the best classical strategies. For example, with respect to the task of phase estimation, the maximum precision (the Heisenberg limit) is a quadratic gain in precision with respect to the best classical strate…
Quantum metrology is a promising practical use case for quantum technologies, where physical quantities can be measured with unprecedented precision. In lieu of quantum error correction procedures, near term quantum devices are expected to be noisy, and we have to make do with noisy probe states. We prove that, for a set of carefully chosen symmetric probe states that lie within certain quantum error correction codes, quantum metrology exhibits an advantage over classical metrology even after the probe states are corrupted by a constant number of erasure and dephasing errors. These probe state…
Role of quantum correlation in metrology beyond standard quantum limit
研究了存在量子关联时的量子精密测量。基于量子费舍尔信息的量子关联测度使我们能够更深入地了解量子关联是如何在设置精度方面起作用的。我们的分析表明，在量子精密测量中，纠缠和量子关联对提高测量精度起着重要作用。即使在没有纠缠的情况下，量子关联也可以作为超越标准量子极限和达到海森堡极限的资源。清楚地解开量子关联的作用，更严格的界限上的精度推导。
Metrology of quantum imaging schemes
该研究将基于空间关联光子对的量子成像方案转化为量子多参数估计问题，计算量子费希尔信息矩阵，比较鬼成像、双光子成像和未检测光子成像的性能，确定适合特定任务的成像协议，为量子传感技术设计优化提供指南。
Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, quantum metrology for non-Markovian processes is much less explored. In this Letter, we establish a general framework of non-Markovian quantum metrology. For any parametrized non-Markovian process on a finite-dimensional system, we derive a formula for the maximal amount of quantum Fisher information that can be extracted from it by an optimally controlled probe state. In addition, we design an alg…
Quantum metrology concerns estimating a parameter from multiple identical uses of a quantum channel. We extend quantum metrology beyond this standard setting and consider estimation of a physical process with quantum memory, here referred to as a parametrized quantum comb. We present a theoretic framework of metrology of quantum combs, and derive a general upper bound of the comb quantum Fisher information. The bound can be operationally interpreted as the quantum Fisher information of a memoryless quantum channel times a dimensional factor. We then show an example where the bound can be attai…
Recently, we find a physical limit on energy consumption of quantum metrology, and demonstrate that it essentially arises from the erasure of quantum Fisher information (QFI) which determines the best achievable measurement precision. Here, we provide more details in order to further elaborate the essence of this principle.
Quantum metrology exploits quantum correlations in specially prepared entangled or other non-classical states to perform measurements that exceed the standard quantum limit. Typically though, such states are hard to engineer, particularly when larger numbers of resources are desired. As an alternative, this paper aims to establish quantum jump metrology which is based on generalised sequential measurements as a general design principle for quantum metrology and discusses how to exploit open quantum systems to obtain a quantum enhancement. By analysing a simple toy model, we illustrate that par…
Experimentally achieving the precision that standard quantum metrology schemes promise is always challenging. Recently, additional controls were applied to design feasible quantum metrology schemes. However, these approaches generally does not consider ease of implementation, raising technological barriers impeding its realization. In this paper, we circumvent this problem by applying closed-loop learning control to propose a practical controlled sequential scheme for quantum metrology. Purity loss of the probe state, which relates to quantum Fisher information, is measured efficiently as the …
We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-…
The simultaneous quantum estimation of multiple parameters can provide a better precision than estimating them individually. This is an effect that is impossible classically. We review the rich background of multi-parameter quantum metrology, some of the main results in the field and its recent advances. We close by highlighting future challenges and open questions.
Metrology of Gravitational Effects with Mechanical Quantum Systems
本文探讨了机械量子系统在引力效应测量中的应用潜力，分析了推进精密传感与量子引力研究所面临的关键挑战及潜在解决方案。
Quantum steering is an important correlation in quantum information theory. A recent work [Nat. Commun. 12, 2410 (2021)] showed that quantum steering is also useful for quantum metrology. Here, we extend the exploration of steering-enhanced quantum metrology from single noiseless phase shifts to superpositions of noisy phase shifts. As concrete examples, we consider a control system that manipulates a target system to pass through a superposition of either dephased or depolarized phase shifts channels. We show that using such superpositions of noisy phase shifts can suppress the effects of noi…
By using highly entangled states, quantum metrology guarantees precision impossible with classical measurements. Unfortunately such states can be very susceptible to noise, and it is a great challenge of the field to maintain quantum advantage in realistic conditions. In this study we investigate the practicality of graph states for quantum metrology. Graph states are a natural resource for much of quantum information, and here we characterize their quantum Fisher information (QFI) for an arbitrary graph state. We then construct families of graph states which approximately achieves the Heisenb…
Using Entangled Generalized Coherent States for Photonic Quantum Metrology
本文提出在光子量子计量学中引入纠缠广义相干态（EGCS）以改进参数估计，该方案展现出超越经典和海森堡极限的灵敏度，优于纠缠相干态和NOON态，并给出了实验生成该态的方案。
Low-temperature Quantum Metrology Enhanced by Strong Couplings
本研究提出利用强耦合效应消除低温量子计量中的误差发散问题，通过反应坐标映射实现多项式型精度标度，为低温高精度噪声量子计量开辟新途径。
Optimality of the Heisenberg limit for continuous-variable quantum metrology
这篇论文已经撤回的作者由于一个致命的缺陷在中央证明。
Quantum metrology pursues high-precision measurements of physical quantities by using quantum resources. However, the decoherence generally hinders its performance. Previous work found that the metrological error tends to diverge in the long-encoding-time regime due to the Born-Markovian approximate decoherence, which is called the no-go theorem of noisy quantum metrology. Here we propose a Gaussian quantum metrology scheme using bimodal quantized optical fields as the quantum probe. It achieves the precision of a sub-Heisenberg limit in the ideal case. However, the Markovian decoherence cause…
We present an alternative protocol allowing for the preparation of critical states that instead of suffering from the critical slowing-down benefits from the critical speeding-up. Paradoxically, we prepare these states by going away from the critical point which allows for the speed-up. We apply the protocol to the paradigmatic quantum Rabi model and its classical oscillator limit as well as the Lipkin-Meshkov-Glick model. Subsequently, we discuss the application of the adiabatic speed-up protocol in quantum metrology and compare its performance with critical quantum metrology. We show that cr…
In this article we study the role that quantum resources play in quantum error correction assisted quantum metrology (QECQM) schemes. We show that there exist classes of such problems where entanglement is not necessary to retrieve noise free evolution and Heisenberg scaling in the long time limit. Over short time scales, noise free evolution is also possible even without any form of quantum correlations. In particular, for qubit probes, we show that whenever noise free quantum metrology is possible via QECQM, entanglement free schemes over long time scales and correlation free schemes over sh…
Enhancing Quantum Metrology by Quantum Resonance Dynamics
本研究提出一种基于周期驱动自旋系统高阶量子共振的量子计量协议，可规避制备高保真纠缠态、读出噪声及噪声环境禁规定理三大障碍，实现海森堡标度精度且抗马尔可夫噪声，可在现有平台验证。
Quantum Optical Metrology -- The Lowdown on High-N00N States
光的量子态，如压缩态或纠缠态，可以用来进行测量（计量学），产生图像，并以远远超过经典可能的精度感测物体，也超过了曾经被认为是可能的量子力学。其主要思想是利用量子效应克服计量学中的散粒噪声极限和成像和传感中的瑞利衍射极限。近年来，随着来自快速发展的光学量子信息处理领域的思想的涌入，量子光学计量学得到了推动。这两个研究领域都利用了光的量子纠缠态的创造和操纵。我们将回顾量子光学计量学这一令人兴奋的新领域的一些最新理论和实验进展，重点介绍利用特定双模纠缠光子态-High-N 00 N态的例子。
We establish the multiparameter quantum Cramér-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright sources, the Cramér-Rao bound is independent of the source separation, which confirms that the Rayleigh resolution limit is just an artifact of the conventional direct imaging and can be overcome with an adequate strategy. For the general case of unequally bright sources, the amount of information one can gain about the separation falls to zero, but we show that …
Quantum metrology overcomes standard precision limits and plays a central role in science and technology. Practically it is vulnerable to imperfections such as decoherence. Here, we demonstrate quantum metrology for noisy channels such that entanglement with ancillary qubits enhances the quantum Fisher information for phase estimation but not otherwise. Our photonic experiment covers a range of noise for various types of channels, including for two randomly alternating channels such that assisted entanglement fails for each noisy channel individually. We have simulated noisy channels by implem…
Quantum metrology
我们指出了一个一般的框架，包括大多数情况下，量子效应使精度的增加时，估计参数（量子精密测量）。典型的量子精度增强是系统被采样次数的平方根的数量级。我们证明，这是最佳的，我们指出了不同的策略（经典和量子），允许达到这个界限。
Graph states are a unique resource for quantum information processing, such as measurement-based quantum computation. Here, we theoretically investigate using continuous-variable graph states for single-parameter quantum metrology, including both phase and displacement sensing. We identified the optimal graph states for the two sensing modalities and showed that Heisenberg scaling of the accuracy for both phase and displacement sensing can be achieved with local homodyne measurements.
Quantum Fisher information as the measure of Gaussian quantum correlation: Role in quantum metrology
我们引入了一种基于量子费舍尔信息的高斯量子关联测度。对于二分高斯态，由于其中一方的局域幺正演化而产生的最小量子费舍尔信息可靠地量化了量子关联。在量子精密测量中，这种测量方法成为研究量子相关性在设定测量精度中所起作用的工具。特别是，可以更深入地了解量子相关性如何有助于提高测量精度。我们的分析表明，不仅纠缠，而且量子关联起着重要的作用，以提高双精度。在揭示量子关联的基本机制的基础上，我们指出，在量子精密测量中，即使在没有纠缠的情况下，量子关联也可以作为突破标准量子极限和达到海森堡极限的资源。
Existence of universal resource and uselessness of too entangled states for quantum metrology
本文证明了线性哈密顿量量子计量中存在通用资源态，并指出高度纠缠态及随机纯态对量子计量无用，强化了纠缠无用性结论。
Interpreting Quantum Discord in Quantum Metrology
多体量子系统显示出不允许经典解释的性质。特别是，即使是非纠缠态也可以享受一种称为量子不和谐的量子关联。我讨论了最近的一些结果的作用，量子不和谐的计量学。给定干涉相位估计协议，其中哈密顿量最初是未知的实验，量子不和谐的探测状态量化的最小精度的估计。这提供了一个广泛研究的信息理论量的物理解释。
Quantum metrology in the noisy intermediate-scale quantum era
本文综述了量子计量学的原理与应用，重点探讨了在现实噪声退相干环境下克服不可行定理、实现量子测量高精度的方法及主动控制策略。
Quantum metrology allows us to attain a measurement precision that surpasses the classically achievable limit by using quantum characters. The metrology precision is raised from the standard quantum limit (SQL) to the Heisenberg limit (HL) by using entanglement. However, it was reported that the HL returns to the SQL in the presence of local dephasing environments under the long encoding-time condition. We evaluate here the exact impacts of local dissipative environments on quantum metrology, based on the Ramsey interferometer. It is found that the HL is asymptotically recovered under the long…
We study very generally to what extent the uncertainty with which a phase shift can be estimated in quantum metrology can be reduced by extending the Hamiltonian that generates the phase shift to an ancilla system with a Hilbert space of arbitrary dimension, and allowing arbitrary interactions between the original system and the ancilla. Such Hamiltonian extensions provide a general framework for open quantum systems, as well as for "non-linear metrology schemes" that have been investigated over the last few years. We prove that such Hamiltonian extensions cannot improve the sensitivity of the…
We consider a cryptographically motivated framework for quantum metrology in the presence of a malicious adversary. We begin by devising an estimation strategy for a (potentially) altered resource (due to a malicious adversary) and quantify the amount of bias and the loss in precision as a function of the introduced uncertainty in the resource. By incorporating an appropriate cryptographic protocol, the uncertainty in the resource can be bounded with respect to the soundness of the cryptographic protocol. Thus the effectiveness of the quantum metrology problem can be directly related to the ef…
We address the relation between quantum metrological resolution and coherence. We examine this dependence in two manners: we develop a quantum Wiener-Kintchine theorem for a suitable model of quantum ruler, and we compute the Fisher information. The two methods have the virtue of including both the contributions of probe and measurement on an equal footing. We illustrate this approach with several examples of linear and nonlinear metrology. Finally, we optimize resolution regarding coherence as a finite resource.
In quantum metrology, quantum probe states are capable of estimating unknown physical parameters to precisions beyond classical limits. What qualities do such states possess? Here we relate the performance of a probe state at estimating a parameter $ϕ$ -- as quantified by the quantum Fisher information -- to the amount of purity it loses when $ϕ$ undergoes statistical fluctuation. This indicates that the better a state is for estimating $ϕ$, the more it decoheres when $ϕ$ is subject to noise.
Adaptive quantum channel discrimination using methods of quantum metrology
本文提出基于量子计量方法的高效算法，用于实现最优自适应量子信道鉴别策略，揭示了信道鉴别与估计问题之间的结构相似性。
Error-mitigated quantum metrology via enhanced virtual purification
本文提出增强虚拟通道净化方法，通过提升虚拟态净化效果，提高量子计量的精度和鲁棒性，适用于单参数和多参数任务，并拓展至更广泛的量子信息领域。
Quantum metrology: why entanglement?
我们展示了为什么以及何时需要纠缠来进行量子增强的精确测量，以及哪种类型的纠缠是有用的。我们给出了一个简单，直观的结构，显示纠缠如何将并行的估计策略转换为连续的相同精度。我们采用这种论点来概括传统的量子精密测量，以确定一类噪声的影响可以很容易地管理，并处理的情况下，不可区分的探针（如光干涉）。
Distributed multi-parameter quantum metrology with a superconducting quantum network
本文展示了一种基于超导量子网络的分布式多参数量子计量学方法，通过增强控制顺序协议实现了对远程矢量场的高精度测量，精度提升达13.72 dB。
The critical quantum metrology, which exploits the quantum phase transition for high precision measurement, has gained increasing attention recently. The critical quantum metrology with the continuous quantum phase transition, however, is experimentally very challenging since the continuous quantum phase transition only exists at the thermal dynamical limit. Here, we propose an adiabatic scheme on a perturbed Ising spin model with the first order quantum phase transition. By employing the Landau-Zener anticrossing, we can not only encode the unknown parameter in the ground state but also tune …
The best Fisher is upstream: data processing inequalities for quantum metrology
我们将经典的数据处理不等式应用到量子精密测量中，以表明操纵来自量子测量的经典信息不能帮助估计编码在量子态中的参数。我们进一步推导了一个量子数据处理不等式，证明了量子数据的相干操作也不能提高估计的精度。此外，我们评论必要的假设，以达到这些不平等，以及如何可以避免提供见解的增强程序是不能证明是错误的。
We develop a variational principle to determine the quantum controls and initial state which optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are in general dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via the Floquet engineering. In particular, we find for magnetometry with a t…
Quantum Metrology is one of the most promising application of quantum technologies. The aim of this research field is the estimation of unknown parameters exploiting quantum resources, whose application can lead to enhanced performances with respect to classical strategies. Several physical quantum systems can be employed to develop quantum sensors, and photonic systems represent ideal probes for a large number of metrological tasks. Here we review the basic concepts behind quantum metrology and then focus on the application of photonic technology for this task, with particular attention to ph…
A quantum metrology scheme can be decomposed into three quantum tasks: state preparation, parameter encoding and measurements. Consequently, it is imperative to have access to the technologies which can execute the aforementioned tasks to fully implement a quantum metrology scheme. In the absence of one or more of these technologies, one can proceed by delegating the tasks to a third party. However, doing so has security ramifications: the third party can bias the result or leak information. In this article, we outline different scenarios where one or more tasks are delegated to an untrusted (…
Quantum metrology enhanced by effective time reversal
通过有效时间反演提升量子测量精度，涵盖回声计量、弱值放大、闭环时间曲线和不定因果顺序四种策略。
Stochastic approach for quantum metrology with generic Hamiltonians
针对通用哈密顿量缺乏变分量子计量方案的问题，本文提出基于量子线路的随机参数平移规则，用于计算量子Fisher信息，并在磁场估计中验证其优于标准参数平移规则。
Differential Evolution for Many-Particle Adaptive Quantum Metrology
我们设计了强大的算法，基于差分进化的自适应多粒子量子精密测量。我们的新方法为反馈控制提供了自适应量子精密测量策略，这些策略的效率更高，并且超过了基于粒子群优化的方法中产生的几十个粒子的限制。我们将我们的方法应用于量子增强相位估计的二进制决策树模型以及一个新问题：用于自适应估计量子硬币在量子行走中的未知偏差的决策树，并展示了如何通过实验实现后一种情况。
No-signaling bounds for quantum cloning and metrology
超光速通信的不可能性是物理学的一个基本原理。在这里，我们表明，这一原则的基础性能的几个基本任务，在量子信息处理和量子精密测量。特别是，我们推导出严格的概率克隆和超复制，符合相应的最佳可实现的并行性和速率的无信号范围。在量子精密测量的背景下，我们推导出海森堡极限从无信号原理的某些情况下，包括参考系对齐和极大似然状态估计。我们阐述了渐近相位协变克隆和相位估计的等价性，为不同的品质因数。
Quantum-dense metrology (QDM) constitutes a special case of quantum metrology in which two orthogonal phase space projections of a signal are simultaneously sensed beyond the shot noise limit. Previously it was shown that the additional sensing channel that is provided by QDM contains information that can be used to identify and to discard corrupted segments from the measurement data. Here, we demonstrate a proof-of-principle experiment in which this information is used for improving the sensitivity without discarding any measurement segments. Our measurement reached sub-shot-noise performance…
Metrology for Quantum Hardware Standardization -- Charting a Pathway: A Strategic Review
探讨量子力学发展下计量与量子技术关系转变，研究量子计算模式所需计量和精密测量能力及电学计量贡献，讨论跨平台测量需求与标准化机会。
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