1
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Arvidsson-Shukur DRM, McConnell AG, Yunger Halpern N. Nonclassical Advantage in Metrology Established via Quantum Simulations of Hypothetical Closed Timelike Curves. PHYSICAL REVIEW LETTERS 2023; 131:150202. [PMID: 37897785 DOI: 10.1103/physrevlett.131.150202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2022] [Revised: 09/08/2023] [Accepted: 09/11/2023] [Indexed: 10/30/2023]
Abstract
We construct a metrology experiment in which the metrologist can sometimes amend the input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change the input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist's winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.
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Affiliation(s)
| | - Aidan G McConnell
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
- Laboratory for X-ray Nanoscience and Technologies, Paul Scherrer Institut, 5232 Villigen, Switzerland
- Department of Physics and Quantum Center, Eidgenössische Technische Hochschule Zürich, CH-8093 Zürich, Switzerland
| | - Nicole Yunger Halpern
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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2
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Ho LB. No-go result for quantum postselection measurements of a rank-
m
degenerate subspace. PHYSICAL REVIEW A 2023; 107:042204. [DOI: 10.1103/physreva.107.042204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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3
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Li J, Niu Y, Wang X, Qin L, Li XQ. Quantum-coherence-free precision metrology by means of difference-signal amplification. Sci Rep 2023; 13:4688. [PMID: 36949235 PMCID: PMC10033826 DOI: 10.1038/s41598-023-31787-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Accepted: 03/17/2023] [Indexed: 03/24/2023] Open
Abstract
The novel weak-value-amplification (WVA) scheme of precision metrology is deeply rooted in the quantum nature of destructive interference between the pre- and post-selection states. And, an alternative version, termed as joint WVA (JWVA), which employs the difference-signal from the post-selection accepted and rejected results, has been found possible to achieve even better sensitivity (two orders of magnitude higher) under some technical limitations (e.g. misalignment errors). In this work, after erasing the quantum coherence, we analyze the difference-signal amplification (DSA) technique, which serves as a classical counterpart of the JWVA, and show that similar amplification effect can be achieved. We obtain a simple expression for the amplified signal, carry out characterization of precision, and point out the optimal working regime. We also discuss how to implement the post-selection of a classical mixed state. The proposed classical DSA technique holds similar technical advantages of the JWVA and may find interesting applications in practice.
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Affiliation(s)
- Jialin Li
- Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300072, China
| | - Yazhi Niu
- Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300072, China
| | - Xinyi Wang
- Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300072, China
| | - Lupei Qin
- Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300072, China.
| | - Xin-Qi Li
- Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300072, China.
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4
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Toward incompatible quantum limits on multiparameter estimation. Nat Commun 2023; 14:1021. [PMID: 36823170 PMCID: PMC9950091 DOI: 10.1038/s41467-023-36661-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 02/10/2023] [Indexed: 02/25/2023] Open
Abstract
Achieving the ultimate precisions for multiple parameters simultaneously is an outstanding challenge in quantum physics, because the optimal measurements for incompatible parameters cannot be performed jointly due to the Heisenberg uncertainty principle. In this work, a criterion proposed for multiparameter estimation provides a possible way to beat this curse. According to this criterion, it is possible to mitigate the influence of incompatibility meanwhile improve the ultimate precisions by increasing the variances of the parameter generators simultaneously. For demonstration, a scheme involving high-order Hermite-Gaussian states as probes is proposed for estimating the spatial displacement and angular tilt of light at the same time, and precisions up to 1.45 nm and 4.08 nrad are achieved in experiment simultaneously. Consequently, our findings provide a deeper insight into the role of Heisenberg uncertainty principle in multiparameter estimation, and contribute in several ways to the applications of quantum metrology.
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5
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Abstract
The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving N probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections—with global control operations, the ideal sensitivity (e.g., the Heisenberg scaling) can always be recovered in the asymptotic N limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision. The effects of detection noise on quantum metrology performances have not been rigorously investigated yet. Here, the authors fill this gap by generalising the quantum Fisher information to the case of noisy readout, and showing the consequences the imperfect measurements bring.
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6
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Lupu-Gladstein N, Yilmaz YB, Arvidsson-Shukur DRM, Brodutch A, Pang AOT, Steinberg AM, Halpern NY. Negative Quasiprobabilities Enhance Phase Estimation in Quantum-Optics Experiment. PHYSICAL REVIEW LETTERS 2022; 128:220504. [PMID: 35714243 DOI: 10.1103/physrevlett.128.220504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2021] [Accepted: 03/21/2022] [Indexed: 06/15/2023]
Abstract
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 PPA, we measure a wave plate's birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter's amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA's metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.
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Affiliation(s)
- Noah Lupu-Gladstein
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Y Batuhan Yilmaz
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | | | - Aharon Brodutch
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Arthur O T Pang
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Aephraim M Steinberg
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Nicole Yunger Halpern
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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7
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Kim Y, Yoo SY, Kim YH. Heisenberg-Limited Metrology via Weak-Value Amplification without Using Entangled Resources. PHYSICAL REVIEW LETTERS 2022; 128:040503. [PMID: 35148150 DOI: 10.1103/physrevlett.128.040503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
Weak-value amplification (WVA) provides a way for amplified detection of a tiny physical signal at the expense of a lower detection probability. Despite this trade-off, due to its robustness against certain types of noise, WVA has advantages over conventional measurements in precision metrology. Moreover, it has been shown that WVA-based metrology can reach the Heisenberg limit using entangled resources, but preparing macroscopic entangled resources remains challenging. Here, we demonstrate a novel WVA scheme based on iterative interactions, achieving the Heisenberg-limited precision scaling without resorting to entanglement. This indicates that the perceived advantages of the entanglement-assisted WVA are in fact due to iterative interactions between each particle of an entangled system and a meter, rather than coming from the entanglement itself. Our work opens a practical pathway for achieving the Heisenberg-limited WVA without using fragile and experimentally demanding entangled resources.
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Affiliation(s)
- Yosep Kim
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Seung-Yeun Yoo
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Yoon-Ho Kim
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
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8
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Song M, Steinmetz J, Zhang Y, Nauriyal J, Lyons K, Jordan AN, Cardenas J. Enhanced on-chip phase measurement by inverse weak value amplification. Nat Commun 2021; 12:6247. [PMID: 34716353 PMCID: PMC8556267 DOI: 10.1038/s41467-021-26522-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Accepted: 10/05/2021] [Indexed: 12/01/2022] Open
Abstract
Optical interferometry plays an essential role in precision metrology such as in gravitational wave detection, gyroscopes, and environmental sensing. Weak value amplification enables reaching the shot-noise-limit of sensitivity, which is difficult for most optical sensors, by amplifying the interferometric signal without amplifying certain technical noises. We implement a generalized form of weak value amplification on an integrated photonic platform with a multi-mode interferometer. Our results pave the way for a more sensitive, robust, and compact platform for measuring phase, which can be adapted to fields such as coherent communications and the quantum domain. In this work, we show a 7 dB signal enhancement in our weak value device over a standard Mach-Zehnder interferometer with equal detected optical power, as well as frequency measurements with 2 kHz sensitivity by adding a ring resonator.
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Affiliation(s)
- Meiting Song
- The Institute of Optics, University of Rochester, Rochester, NY, 14627, USA
| | - John Steinmetz
- Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627, USA
| | - Yi Zhang
- The Institute of Optics, University of Rochester, Rochester, NY, 14627, USA
| | - Juniyali Nauriyal
- The Institute of Optics, University of Rochester, Rochester, NY, 14627, USA
- Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY, 14627, USA
| | - Kevin Lyons
- Hoplite AI, 2 Fox Glen Ct., Clifton Park, NY, 12065, USA
| | - Andrew N Jordan
- Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627, USA
- Institute for Quantum Studies, Chapman University, Orange, CA, 92866, USA
| | - Jaime Cardenas
- The Institute of Optics, University of Rochester, Rochester, NY, 14627, USA.
- Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627, USA.
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9
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Li Z, Xu Y, Ma K, Liu L, Xi J, Guan T, Li F, Zhou C, Zhong S, He Y. In situ detection of electrochemical reaction by weak measurement. OPTICS EXPRESS 2021; 29:19292-19304. [PMID: 34266041 DOI: 10.1364/oe.426345] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Accepted: 05/27/2021] [Indexed: 06/13/2023]
Abstract
In the field of electrochemical energy storage systems, the use of in situ detection technology helps to study the mechanism of electrochemical reaction. Our group has previously in situ detected the electrochemical reaction in vanadium flow batteries by total internal reflection (TIR) imaging. In order to further improve the detection resolution, in this study, the weak measurement (WM) method was introduced to in situ detect the electrochemical reaction during the linear sweep voltammetry or the cyclic voltammetry tests with quantitative measurement of the absolute current density, which lays a foundation for replacing the TIR for two-dimensional imaging of electrochemical reactions in vanadium flow batteries, oxygen/hydrogen evolution reaction, surface treatments, electrochemical corrosion and so on.
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10
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Yin P, Zhang WH, Xu L, Liu ZG, Zhuang WF, Chen L, Gong M, Ma Y, Peng XX, Li GC, Xu JS, Zhou ZQ, Zhang L, Chen G, Li CF, Guo GC. Improving the precision of optical metrology by detecting fewer photons with biased weak measurement. LIGHT, SCIENCE & APPLICATIONS 2021; 10:103. [PMID: 34001846 PMCID: PMC8128924 DOI: 10.1038/s41377-021-00543-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Revised: 04/15/2021] [Accepted: 04/21/2021] [Indexed: 06/12/2023]
Abstract
In optical metrological protocols to measure physical quantities, it is, in principle, always beneficial to increase photon number n to improve measurement precision. However, practical constraints prevent the arbitrary increase of n due to the imperfections of a practical detector, especially when the detector response is dominated by the saturation effect. In this work, we show that a modified weak measurement protocol, namely, biased weak measurement significantly improves the precision of optical metrology in the presence of saturation effect. This method detects an ultra-small fraction of photons while maintains a considerable amount of metrological information. The biased pre-coupling leads to an additional reduction of photons in the post-selection and generates an extinction point in the spectrum distribution, which is extremely sensitive to the estimated parameter and difficult to be saturated. Therefore, the Fisher information can be persistently enhanced by increasing the photon number. In our magnetic-sensing experiment, biased weak measurement achieves precision approximately one order of magnitude better than those of previously used methods. The proposed method can be applied in various optical measurement schemes to remarkably mitigate the detector saturation effect with low-cost apparatuses.
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Grants
- This work was supported by the National Key Research and Development Program of China (Nos. 2016YFA0302700, 2017YFA0304100), National Natural Science Foundation of China (Grant Nos. 11874344, 61835004, 61327901, 11774335, 91536219, 11821404), Key Research Program of Frontier Sciences, CAS (No. QYZDY-SSW-SLH003), Anhui Initiative in Quantum Information Technologies (AHY020100, AHY060300), the Fundamental Research Funds for the Central Universities (Grant No. WK2030020019, WK2470000026), Science Foundation of the CAS (No. ZDRW-XH-2019-1).
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Affiliation(s)
- Peng Yin
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Wen-Hao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Liang Xu
- National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
| | - Ze-Gang Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Wei-Feng Zhuang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Lei Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Ming Gong
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Yu Ma
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Xing-Xiang Peng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Gong-Chu Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Zong-Quan Zhou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
| | - Geng Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China.
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China.
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
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11
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Beating Standard Quantum Limit with Weak Measurement. ENTROPY 2021; 23:e23030354. [PMID: 33809680 PMCID: PMC8002236 DOI: 10.3390/e23030354] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Revised: 02/27/2021] [Accepted: 03/04/2021] [Indexed: 11/16/2022]
Abstract
Weak measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of a reduced rate of acquiring data, which leads to an increasing uncertainty to determine the level of meter shift. From this point of view, a number of theoretical works have suggested that weak measurements cannot improve the precision, or even damage the metrology information due to the post-selection. In this review, we give a comprehensive analysis of the weak measurements to justify their positive effect on prompting measurement precision. As a further step, we introduce two modified weak measurement protocols to boost the precision beyond the standard quantum limit. Compared to previous works beating the standard quantum limit, these protocols are free of using entangled or squeezed states. The achieved precision outperforms that of the conventional method by two orders of magnitude and attains a practical Heisenberg scaling up to n=106 photons.
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12
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Stárek R, Mičuda M, Hošák R, Ježek M, Fiurášek J. Experimental entanglement-assisted weak measurement of phase shift. OPTICS EXPRESS 2020; 28:34639-34655. [PMID: 33182927 DOI: 10.1364/oe.403711] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 10/14/2020] [Indexed: 06/11/2023]
Abstract
Weak value amplification is a popular method in quantum metrology for enhancing the sensitivity at the expense of the signal intensity. Recently, it was suggested that the trade-off between signal intensity and sensitivity can be improved by using an entangled auxiliary system. Here, we experimentally investigate such entanglement-assisted weak measurement of small conditional phase shifts induced by an interaction between ancilla and meter qubits. We utilize entangled photon pairs and implement the required three-qubit quantum logic circuit with linear optics. The circuit comprises a two-qubit controlled phase gate and a three-qubit controlled-controlled phase gate with fully tunable conditional phase shifts. We fully characterize the output states of our circuit by quantum state tomography and perform a comprehensive analysis of the trade-off between the measurement sensitivity and the success probability of the protocol. The observed experimental results are in good qualitative agreement with theoretical predictions, but the overall performance of our setup is limited by various experimental imperfections. We provide a detailed theoretical analysis of the influence of dephasing of the entangled ancilla state, which is one of the main sources of imperfections in the experiment. We also discuss the ultimate scaling with the dimension of the entangled ancilla system.
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13
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Xu L, Liu Z, Datta A, Knee GC, Lundeen JS, Lu YQ, Zhang L. Approaching Quantum-Limited Metrology with Imperfect Detectors by Using Weak-Value Amplification. PHYSICAL REVIEW LETTERS 2020; 125:080501. [PMID: 32909785 DOI: 10.1103/physrevlett.125.080501] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 07/24/2020] [Indexed: 06/11/2023]
Abstract
Weak-value amplification (WVA) is a metrological protocol that amplifies ultrasmall physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photodetection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is 6 times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.
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Affiliation(s)
- Liang Xu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Zexuan Liu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - George C Knee
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Jeff S Lundeen
- Max Planck Centre for Extreme and Quantum Photonics, Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - Yan-Qing Lu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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14
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Arvidsson-Shukur DRM, Yunger Halpern N, Lepage HV, Lasek AA, Barnes CHW, Lloyd S. Quantum advantage in postselected metrology. Nat Commun 2020; 11:3775. [PMID: 32728082 PMCID: PMC7391714 DOI: 10.1038/s41467-020-17559-w] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 07/08/2020] [Indexed: 11/08/2022] Open
Abstract
In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantum-mechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool.
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Affiliation(s)
- David R M Arvidsson-Shukur
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK.
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
| | - Nicole Yunger Halpern
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, 02138, USA
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Hugo V Lepage
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Aleksander A Lasek
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Crispin H W Barnes
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Seth Lloyd
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
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15
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Duan Y, Hosseini M, Beck KM, Vuletić V. Heralded Interaction Control between Quantum Systems. PHYSICAL REVIEW LETTERS 2020; 124:223602. [PMID: 32567901 DOI: 10.1103/physrevlett.124.223602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Abstract
Quantum mechanical expectation values for subsets can differ substantially from those for the whole ensemble. This implies that the effect of interactions between two systems can be altered substantially by conditioning. Here, we experimentally demonstrate that, for two light fields ψ_{S} (signal) and ψ_{A} (ancilla) that have only weakly interacted with one another, subsequent measurements on the ancilla can produce substantial conditional amplification, attenuation, or phase shift of ψ_{S}. We observe conditional signal power changes over a large range of 30, and phase shift up to π/2, induced by measurements in ancilla bases that differ only slightly from one another. The method is generically applicable to a variety of systems, and allows one to modify or boost a given interaction by trading in success probability for interaction strength.
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Affiliation(s)
- Yiheng Duan
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mahdi Hosseini
- Birck Nanotechnology Center, School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | | | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Gillmer SR, Martínez-Rincón J, Ellis JD. Anomalous vibration suppression in a weak-value-emulated heterodyne roll interferometer. OPTICS EXPRESS 2018; 26:29311-29318. [PMID: 30470096 DOI: 10.1364/oe.26.029311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2018] [Accepted: 09/26/2018] [Indexed: 06/09/2023]
Abstract
We experimentally validate the vibration suppression capabilities of a weak-value-like protocol. The phase-sensitive heterodyne technique exhibits advantageous characteristics of a weak measurement including anomalous amplification in sensitivity and technical noise suppression. It does not, however, leverage the entanglement between the system and meter to amplify the signal of interest, as is typical in a weak measurement. In this formalism, we demonstrate an amplification in sensitivity to the roll angle of over 700 times. High precision roll experiments anchor numerical simulations to show that the interferometer outperforms standard interferometry by a factor of 500 in terms of peak-to-peak noise amplitude. During the measurement of a rolling stage, technical noise - primarily in the form of vibrations - is substantially attenuated. This is the first demonstration of vibration suppression capabilities that are inherent to the light from a metrology instrument instead of achieved via mechanical damping. The emulation presented in this work also identifies an avenue to achieve anomalous amplification outside of the standard weak measurement protocol.
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Vaidman L. Weak value controversy. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2016.0395. [PMID: 28971947 PMCID: PMC5628259 DOI: 10.1098/rsta.2016.0395] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 05/30/2017] [Indexed: 06/07/2023]
Abstract
Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide useful amplification techniques for precision measurements of small effects in many realistic situations. The statistical nature of weak values is questioned. Although measuring weak values requires an ensemble, it is argued that the weak value, similarly to an eigenvalue, is a property of a single pre- and post-selected quantum system.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
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Affiliation(s)
- L Vaidman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel
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