In the context of phase estimation with Gaussian states, we introduce a quantifiable definition of metrological advantage that takes into account thermal noise in the preparation procedure. For a broad set of states, \textit{isotropic non-pure Gaussian states}, we show that squeezing is not only necessary, but sufficient, to achieve metrological advantage. We interpret our results in the framework of resource theory, and discuss possible sources of advantage other than squeezing. Our work is a step towards using phase estimation with pure and mixed state to define and quantify nonclassicality. This work is complementary with studies that defines nonclassicality using quadrature displacement estimation.
Comment on J.Qin et al., Unconditional and Robust Quantum Metrological Advantage beyond N00N States, PRL 130, 070801 (2023) and J.A. H. Nielsen et.al., Deterministic Quantum Phase Estimation beyond N00N States. PRL 130, 123603 (2023)
The well known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly sensitive non-Gaussian states. Here, we introduce a class of metrological nonlinear squeezing parameters obtained by analytical optimization of measurement observables among a given set of accessible (possibly nonlinear) operators. This allows for the metrological characterization of non-Gaussian quantum states of discrete and continuous variables. Our results…
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterises the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP),…
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…
Causal Fisher-Information Inequalities: Classical Causal Model Falsification and Metrological Advantage
Institute for Convergence Research and Education in Advanced Technology, Yonsei University（延世大学先进技术与教育融合研究所）；Department of Quantum Information, Yonsei University（延世大学量子信息系）；Agency for Defense Development（国防发展局）；University of Science and Technology（科学技术大学）
Quantum metrology employs quantum resources to enhance the measurement sensitivity beyond that can be achieved classically. While multi-photon entangled NOON states can in principle beat the shot-noise limit and reach the Heisenberg limit, high NOON states are difficult to prepare and fragile to photon loss which hinders it from reaching unconditional quantum metrological advantages. Here, we combine the idea of unconventional nonlinear interferometers and stimulated emission of squeezed light, previously developed for photonic quantum computer Jiuzhang, to propose and realize a new scheme tha…
Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学和量子信息研究所）；Faculty of Physics, University of Warsaw（华沙大学物理系）；Qilimanjaro Quantum Tech（基利马扎罗量子技术）
International Quantum Academy（国际量子研究院）；Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学深圳量子科学与工程研究院）；Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学广东省量子科学与工程重点实验室）；CAS Key Laboratory of Quantum Information, University of Science and Technology of China（中国科学院量子信息重点实验室，中国科学技术大学）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）
Precise measurement is crucial to science and technology. However, the rule of nature imposes various restrictions on the precision that can be achieved depending on specific methods of measurement. In particular, quantum mechanics poses the ultimate limit on precision which can only be approached but never be violated. Depending on analytic techniques, these bounds may not be unique. Here, in view of prior information, we investigate systematically the precision bounds of the total mean-square error of vector parameter estimation which contains $d$ independent parameters. From quantum Ziv-Zak…
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 identify the large-$N$ scaling of the metrological quantum gain offered by over-squeezed spin states that are accessible by one-axis-twisting, as a function of the preparation time. We further determine how the scaling is modified by relevant decoherence processes and predict a discontinuous change of the quantum gain at a critical preparation time that depends on the noise. Our analytical results provide recipes for optimal and feasible implementations of quantum enhancements with non-Gaussian spin states in existing experiments, well beyond the reach of spin squeezing.
Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities -- quantum extensions of probabilities -- engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using P…
Frequency correlations are a versatile and powerful tool which can be exploited to perform spectral analysis of objects whose direct measurement might be unfeasible. This is achieved through a so-called ghost spectrometer, that can be implemented with quantum and classical resources alike. While there are some known advantages associated to either choice, an analysis of their metrological capabilities has not yet been performed. Here we report on the metrological comparison between a quantum and a classical ghost spectrometer. We perform the estimation of the transmittivity of a bandpass filte…
We study the generation of planar quantum squeezed (PQS) states by quantum non-demolition (QND) measurement of a cold ensemble of $^{87}$Rb atoms. Precise calibration of the QND measurement allows us to infer the conditional covariance matrix describing the $F_y$ and $F_z$ components of the PQS, revealing the dual squeezing characteristic of PQS. PQS states have been proposed for single-shot phase estimation without prior knowledge of the likely values of the phase. We show that for an arbitrary phase, the generated PQS gives a metrological advantage of at least 3.1 dB relative to classical st…
Very recently, strongly non-Gaussian states have been observed via a direct three-mode spontaneous parametric down-conversion in a superconducting cavity [Phys. Rev. X 10, 011011 (2020)]. The created multi-photon non-Gaussian correlations are attractive and useful for various quantum information tasks. However, how to detect and classify multipartite non-Gaussian entanglement has not yet been completely understood. Here, we present an experimentally practical method to characterize continuous-variable multipartite non-Gaussian entanglement, by introducing a class of nonlinear squeezing paramet…
The force estimation problem in quantum metrology with an arbitrary non-Markovian Gaussian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state and the best measurement. Studying the short time behavior and comparing to regular Markovian dynamics we observe an …
Scientists in quantum technology aspire to quantum advantage: a computational result unattainable with classical computers. Gaussian boson sampling experiment has been already claimed to achieve this goal. In this setup squeezed light states interfere in a mid-sized linear optical network, where multi-photon collisions take place. The exact simulation of the counting statistics of $n$ threshold detectors is far beyond the possibilities of modern supercomputers once $n$ exceeds $100$. Here we challenge quantum advantage for a mid-sized Gaussian boson sampling setup and propose the approximate a…
Lossy bosonic channels play an important role in a number of quantum information tasks, since they well approximate thermal dissipation in an experiment. Here, we characterize their metrological power in the idler-free and entanglement-assisted cases, using respectively single- and two-mode Gaussian states as probes. In the problem of estimating the lossy parameter, we study the energy-constrained quantum Fisher information (QFI) for generic temperature and lossy parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum…
Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the phase of an electromagnetic field, and single-shot measurements of this phase are necessary. While there are measurements able to estimate the phase of light in a single shot with small uncertainties, demonstrations of near-optimal single-shot measurements for an unknown phase of a coherent state remain elusive. Here, we propose and demonstrate strategies f…
Recent claims of achieving exponential quantum advantage have attracted attention to Gaussian boson sampling (GBS), a potential application of which is dense subgraph finding. We investigate the effects of sources of error including loss and spectral impurity on GBS applied to dense subgraph finding algorithms. We find that the effectiveness of these algorithms is remarkably robust to errors, to such an extent that there exist efficient classical algorithms that can simulate the underlying GBS. These results imply that the speedup of GBS-based algorithms for the dense subgraph problem over cla…
Learning Unified Control of Intrinsic Nonlinear Spin Dynamics in Atomic Qudits for Magnetometry
College of Physics, Nanjing University of Aeronautics（南京航空航天大学物理学院）；China Mobile (Suzhou) Software Technology Co., Ltd.（中国移动（苏州）软件技术有限公司）；Shanghai Institute of Optics and Fine Mechanics（上海光学精密机械研究所）；Chinese Academy of Sciences（中国科学院）；Key Laboratory of Aerospace Information Sensing（航空航天信息感知重点实验室）
Proofs of the quantum advantage available in imaging or detecting objects under quantum illumination can rely on optimal measurements without specifying what they are. We use the continuous-variable Gaussian quantum information formalism to show that quantum illumination is better for object detection compared with coherent states of the same mean photon number, even for simple direct photodetection. The advantage persists if signal energy and object reflectivity are low and background thermal noise is high. The advantage is even greater if we match signal beam detection probabilities rather t…
The metrological ability of carefully designed probes can be spoilt by the presence of noisy processes occurring during their evolution. The noise is responsible for altering the evolution of the probes in such a way that bear little or no information on the parameter of interest, hence spoiling the signal-to-noise ratio of any possible measurement. Here we show an experiment in which the introduction of an ancilla improves the estimation of an optical phase in the high-noise regime. The advantage is realised by the coherent coupling of the probe and the ancilla at the initialisation and the m…
Squeezing as a catalyst for non-Gaussian advantage in characterization of nonlinear media
Harish-Chandra Research Institute（哈拉·昌德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）；Institute of Physics, Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学物理研究所）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学重点实验室）；Dipartimento di Fisica dell’Università di Milano（米兰大学物理系）
Identifying the boundary beyond which quantum machines provide a computational advantage over their classical counterparts is a crucial step in charting their usefulness. Gaussian Boson Sampling (GBS), in which photons are measured from a highly entangled Gaussian state, is a leading approach in pursuing quantum advantage. State-of-the-art quantum photonics experiments that, once programmed, run in minutes, would require 600 million years to simulate using the best pre-existing classical algorithms. Here, we present substantially faster classical GBS simulation methods, including speed and acc…
Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We pro…
We propose the difference weak measurement scheme, and illustrate its advantages for measuring small longitude phase-shift in high precision. Compared to the standard interferometry and standard weak measurement schemes, the proposed scheme has much higher resolution in present of various practical imperfections, such as alignment error and light intensity variation error. Moreover, we highlight the advantage of utilizing complex weak value, where its imaginary part can reduce the harmful effect induced by channel decoherence. Finally, we propose closed-loop scenario to solve the narrow dynami…
Stochastic signal sensing with finite energy and dead time at the fundamental quantum limit
Chicago Quantum Institute, Pritzker School of Molecular Engineering, University of Chicago（芝加哥量子研究所，普林茨克分子工程学院，芝加哥大学）；Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；Department of Physics, ETH Zürich（苏黎世联邦理工学院物理系）
Quantum metrology offers a quadratic advantage over classical approaches to parameter estimation problems by utilizing entanglement and nonclassicality. However, the hurdle of actually implementing the necessary quantum probe states and measurements, which vary drastically for different metrological scenarios, is usually not taken into account. We show that for a wide range of tasks in metrology, 2D cluster states (a particular family of states useful for measurement-based quantum computation) can serve as flexible resources that allow one to efficiently prepare any required state for sensing,…
