1
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Hofmann HF. Statistical Signatures of Quantum Contextuality. ENTROPY (BASEL, SWITZERLAND) 2024; 26:725. [PMID: 39330060 PMCID: PMC11431591 DOI: 10.3390/e26090725] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2024] [Revised: 08/16/2024] [Accepted: 08/16/2024] [Indexed: 09/28/2024]
Abstract
Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement of the independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood-Dirac quasiprobability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts.
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Affiliation(s)
- Holger F Hofmann
- Graduate School of Advanced Science and Engineering, Hiroshima University, Kagamiyama 1-3-1, Higashi Hiroshima 739-8530, Japan
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2
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Han W, Guo H, Liu Y, Wu J, Zhang Z, Ye Y, Qi J. Magneto-Optical Ceramics with High Transparency for Highly Sensitive Magnetometer via Quantum Weak Measurement. ACS APPLIED MATERIALS & INTERFACES 2024; 16:39551-39560. [PMID: 39037872 DOI: 10.1021/acsami.4c04658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/24/2024]
Abstract
Sensitive magnetometer technology is desirable for biomagnetic field detection and geomagnetic field measuring. Signal amplification materials such as magneto-optical crystals or ceramics are crucial for enhancing detection sensitivity, but severe optical scattering and low Verdet constant further limit its application. To develop high-sensitivity magnetometers for quantum weak measurement schemes, we have conducted investigations on the powder calcining dynamics and prepared a series of high-optical-quality (Ho/Dy)2Zr2O7 transparent ceramic samples. The Verdet constant of magneto-optical materials was measured across a continuous wavelength spectrum, exhibiting a peak at 283 ± 5 rad/(T·m). We further established an electron transition mechanism to elucidate the exceptional magneto-optical attributes of dysprosium. In addition, samples demonstrated superior performance in weak-value amplification, reaching a low detectable magnetic field threshold of 3.5 × 10-8 T and continuously worked over 6 h with high stability. Our work developed a highly sensitive magnetometer using optimized magneto-optical ceramics and provided guidance on design, fabrication, and application for magneto-optical ceramics in quantum weak measurement.
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Affiliation(s)
- Wenhan Han
- College of Physics, Sichuan University, Chengdu 610064, China
- Key Laboratory of High Energy Density Physics of Ministry of Education, Sichuan University, Chengdu 610064, Sichuan China
| | - Hao Guo
- College of Physics, Sichuan University, Chengdu 610064, China
| | - Yurong Liu
- College of Physics, Sichuan University, Chengdu 610064, China
| | - Jiguo Wu
- College of Physics, Sichuan University, Chengdu 610064, China
| | - Zhiyou Zhang
- College of Physics, Sichuan University, Chengdu 610064, China
| | - Yucheng Ye
- School of Biomedical Sciences, LKS Faculty of Medicine, University of Hong Kong, Hong Kong Island 999077, Hong Kong SAR China
| | - Jianqi Qi
- College of Physics, Sichuan University, Chengdu 610064, China
- Key Laboratory of High Energy Density Physics of Ministry of Education, Sichuan University, Chengdu 610064, Sichuan China
- Key Laboratory of Radiation Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, Sichuan China
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3
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Xu L, Zhou M, Tao R, Zhong Z, Wang B, Cao Z, Xia H, Wang Q, Zhan H, Zhang A, Yu S, Xu N, Dong Y, Ren C, Zhang L. Resource-Efficient Direct Characterization of General Density Matrix. PHYSICAL REVIEW LETTERS 2024; 132:030201. [PMID: 38307054 DOI: 10.1103/physrevlett.132.030201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 11/27/2023] [Indexed: 02/04/2024]
Abstract
Sequential weak measurements allow for the direct extraction of individual density-matrix elements, rather than relying on global reconstruction of the entire density matrix, which opens a new avenue for the characterization of quantum systems. Nevertheless, extending the sequential scheme to multiqudit quantum systems is challenging due to the requirement of multiple coupling processes for each qudit and the lack of appropriate precision evaluation. To address these issues, we propose a resource-efficient scheme (RES) that directly characterizes the density matrix of general multiqudit systems while optimizing measurements and establishing a feasible estimation analysis. In the RES, an efficient observable of the quantum system is constructed such that a single meter state coupled to each qudit is sufficient to extract the corresponding density-matrix element. An appropriate model based on the statistical distribution of errors is utilized to evaluate the precision and feasibility of the scheme. We have experimentally applied the RES to the direct characterization of general single-photon qutrit states and two-photon entangled states. The results show that the RES outperforms sequential schemes in terms of efficiency and precision in both weak- and strong-coupling scenarios. This Letter sheds new light on the practical characterization of large-scale quantum systems and the investigation of their nonclassical properties.
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Affiliation(s)
- Liang Xu
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- 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
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Mingti Zhou
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Runxia Tao
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Zhipeng Zhong
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Ben Wang
- 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
| | - Zhiyong Cao
- School of Electronic Control, Chang'an University, Xi'an 710064, China
| | - Hongkuan Xia
- 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
| | - Qianyi Wang
- 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
| | - Hao Zhan
- 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
| | - Aonan Zhang
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - Shang Yu
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - Nanyang Xu
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Ying Dong
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Changliang Ren
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, 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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4
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Pei JH, Chen JF, Quan HT. Exploring quasiprobability approaches to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution. Phys Rev E 2023; 108:054109. [PMID: 38115414 DOI: 10.1103/physreve.108.054109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 10/09/2023] [Indexed: 12/21/2023]
Abstract
In quantum thermodynamics, the two-projective-measurement (TPM) scheme provides a successful description of stochastic work only in the absence of initial quantum coherence. Extending the quantum work distribution to quasiprobability is a general way to characterize work fluctuation in the presence of initial coherence. However, among a large number of different definitions, there is no consensus on the most appropriate work quasiprobability. In this article, we list several physically reasonable requirements including the first law of thermodynamics, time-reversal symmetry, positivity of second-order moment, and a support condition for the work distribution. We prove that the only definition that satisfies all these requirements is the Margenau-Hill (MH) quasiprobability of work. In this sense, the MH quasiprobability of work shows its advantages over other definitions. As an illustration, we calculate the MH work distribution of a breathing harmonic oscillator with initial squeezed states and show the convergence to classical work distribution in the classical limit.
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Affiliation(s)
- Ji-Hui Pei
- School of Physics, Peking University, Beijing 100871, China
| | - Jin-Fu Chen
- School of Physics, Peking University, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
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5
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Yang YH, Zhang BB, Wang XL, Geng SJ, Chen PY. Characterizing an Uncertainty Diagram and Kirkwood-Dirac Nonclassicality Based on Discrete Fourier Transform. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1075. [PMID: 37510021 PMCID: PMC10377937 DOI: 10.3390/e25071075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 07/13/2023] [Accepted: 07/14/2023] [Indexed: 07/30/2023]
Abstract
In this paper, we investigate an uncertainty diagram and Kirkwood-Dirac (KD) nonclassicality based on discrete Fourier transform (DFT) in a d-dimensional system. We first consider the uncertainty diagram of the DFT matrix, which is a transition matrix from basis A to basis B. Here, the bases A, B are not necessarily completely incompatible. We show that for the uncertainty diagram of the DFT matrix, there is no "hole" in the region of the (nA,nB) plane above and on the line nA+nB=d+1. Then, we present where the holes are in the region strictly below the line and above the hyperbola nAnB=d. Finally, we provide an alternative proof of the conjecture about KD nonclassicality based on DFT.
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Affiliation(s)
- Ying-Hui Yang
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
| | - Bing-Bing Zhang
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
| | - Xiao-Li Wang
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
| | - Shi-Jiao Geng
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
| | - Pei-Ying Chen
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
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6
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Okamoto R, Cohen E. Experimentally probing anomalous time evolution of a single photon. PNAS NEXUS 2023; 2:pgad157. [PMID: 37265544 PMCID: PMC10230160 DOI: 10.1093/pnasnexus/pgad157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 04/26/2023] [Accepted: 05/01/2023] [Indexed: 06/03/2023]
Abstract
In quantum mechanics, a quantum system is irreversibly collapsed by a projective measurement. Hence, delicately probing the time evolution of a quantum system holds the key to understanding curious phenomena. Here, we experimentally explore an anomalous time evolution, where, illustratively, a particle disappears from a box and emerges in a different box, with a certain moment in which it can be found in neither of them. In this experiment, we directly probe this curious time evolution of a single photon by measuring up to triple-operator sequential weak values (SWVs) using a novel probeless scheme. The naive interpretation provided by single-operator weak values (WVs) seems to imply the "disappearance" and "re-appearance" of a photon as theoretically predicted. However, double- and triple-operator SWVs, representing temporal correlations between the aforementioned values, show that spatial information about the photon does not entirely vanish in the intermediate time. These results show that local values (in space and time) alone, such as single-operator WVs, cannot fully explain all types of quantum evolution in time-higher order correlations are necessary in general, shedding new light on time evolution in quantum mechanics. The probeless measurement technique proposed here for measuring multiple-operator WVs can be straightforwardly extended to study various other cases of curious quantum evolution in time.
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Affiliation(s)
- Ryo Okamoto
- Department of Electronic Science and Engineering, Kyoto University, Kyoto Daigaku-Katsura, Nishikyo-ku, 615-8510 Kyoto, Japan
- PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, 332-0012 Saitama, Japan
| | - Eliahu Cohen
- Faculty of Engineering and Institute of Nanotechnology and Advanced Materials, Bar Ilan University, 5290002 Ramat Gan, Israel
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7
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Jiang L, Li Z, Li T. Nonlocal generalized quantum measurement of product observables with mixed entanglement. OPTICS EXPRESS 2023; 31:12508-12519. [PMID: 37157409 DOI: 10.1364/oe.487883] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Nonlocal observables of spacelike separated quantum systems in combination with their measurements contribute greatly to quantum theory and its applications. We present a nonlocal generalized quantum measurement protocol for measuring product observables, assisted by a meter in a mixed entangled state rather than maximally or partially entangled pure states. By tuning the entanglement of the meter, measurement strength of arbitrary values can be achieved for nonlocal product observables, since measurement strength equals the concurrence of the meter. Furthermore, we present a specific scheme to measure the polarization of two nonlocal photons using linear optics. We refer to the polarization and spatial-mode degrees of freedom of the same photon pair as the system and the meter, respectively, which significantly simplifies the interaction between the system and the meter. This protocol can be useful for applications involving nonlocal product observables and nonlocal weak values, and for tests of quantum foundations in nonlocal scenarios.
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8
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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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9
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Wang S, Han XH, Li WC, Qian T, Fan X, Xiao Y, Gu YJ. Protecting nonlocal quantum correlations in correlated squeezed generalized amplitude damping channel. Sci Rep 2022; 12:20481. [PMID: 36443637 PMCID: PMC9705301 DOI: 10.1038/s41598-022-24789-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 11/21/2022] [Indexed: 11/29/2022] Open
Abstract
Nonlocal quantum correlations, such as quantum entanglement, quantum steering, and Bell nonlocality, are crucial resources for quantum information tasks. How to protect these quantum resources from decoherence is one of the most urgent problems to be solved. Here, we investigate the evolution of these correlations in the correlated squeezed generalized amplitude damping (SGAD) channel and propose a scheme to protect them with weak measurement (WM) and quantum measurement reversal (QMR). Compared with the results of the uncorrelated SGAD channel, we find that when [Formula: see text], correlation and squeezing effects can prolong the survival time of quantum entanglement, Bell nonlocality, and quantum steering by about 152 times, 207 times, and 10 times, respectively. In addition, local WM and QMR can effectively recover the disappeared nonlocal quantum correlations either in uncorrelated or completely correlated SGAD channels. Moreover, we find that these initial nonlocal quantum correlations could be drastically amplified under the correlated channel. And the steering direction can be flexibly manipulated either by changing the channel parameters or the strength of WM and QMR. These results not only make a step forward in suppressing decoherence and enhancing quantum correlation in noise channels, but also help to develop relevant practical applications.
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Affiliation(s)
- Shuo Wang
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China
| | - Xin-Hong Han
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China
| | - Wei-Chen Li
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China
| | - Tian Qian
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China
| | - Xuan Fan
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China
| | - Ya Xiao
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China.
| | - Yong-Jian Gu
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, 266100, People's Republic of China.
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10
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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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11
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Linear Superposition as a Core Theorem of Quantum Empiricism. UNIVERSE 2022. [DOI: 10.3390/universe8040217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Clarifying the nature of the quantum state |Ψ⟩ is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure—quantum superposition—is based on a set-theoretic creation of ensemble formations and invokes the following three principia: (I) quantum statics, (II) doctrine of the number in the physical theory, and (III) mathematization of matching the two observations with each other (quantum covariance). All of the constructs rest upon a formalization of the minimal experimental entity—the registered micro-event, detector click. This is sufficient for producing the C-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the spatio-temporal concepts. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice.
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12
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De Bièvre S. Complete Incompatibility, Support Uncertainty, and Kirkwood-Dirac Nonclassicality. PHYSICAL REVIEW LETTERS 2021; 127:190404. [PMID: 34797160 DOI: 10.1103/physrevlett.127.190404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2021] [Accepted: 10/08/2021] [Indexed: 06/13/2023]
Abstract
For quantum systems with a finite dimensional Hilbert space of states, we show that the complete incompatibility of two observables-a notion we introduce-is equivalent to the large support uncertainty of all states. The Kirkwood-Dirac (KD) quasiprobability distribution of a state-which depends on the choice of two observables-has emerged in quantum information theory as a tool for assessing nonclassical features of the state that can serve as a resource in quantum protocols. We apply our result to show that, when the two observables are completely incompatible, only states with minimal support uncertainty can be KD classical, all others being KD nonclassical. We illustrate our findings with examples.
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Affiliation(s)
- Stephan De Bièvre
- Univ. Lille, CNRS, Inria, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France
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13
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Zheng Y, Yang M, Liu ZH, Xu JS, Li CF, Guo GC. Detecting momentum weak value: Shack-Hartmann versus a weak measurement wavefront sensor. OPTICS LETTERS 2021; 46:5352-5355. [PMID: 34724473 DOI: 10.1364/ol.439174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
The task of wavefront sensing is to measure the phase of the optical field. Here, we demonstrate that the widely used Shack-Hartmann wavefront sensor detects the weak value of transverse momentum, usually achieved by the method of quantum weak measurement. We extend its input states to partially coherent states and compare it with the weak measurement wavefront sensor, which has a higher spatial resolution but a smaller dynamic range. Since weak values are commonly used in investigating fundamental quantum physics and quantum metrology, our work would find essential applications in these fields.
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14
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Xu L, Xu H, Jiang T, Xu F, Zheng K, Wang B, Zhang A, Zhang L. Direct Characterization of Quantum Measurements Using Weak Values. PHYSICAL REVIEW LETTERS 2021; 127:180401. [PMID: 34767426 DOI: 10.1103/physrevlett.127.180401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Revised: 07/28/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
The time-symmetric formalism endows the weak measurement and its outcome, the weak value, with many unique features. In particular, it allows a direct tomography of quantum states without resorting to complicated reconstruction algorithms and provides an operational meaning to wave functions and density matrices. Here, we propose and experimentally demonstrate the direct tomography of a measurement apparatus by taking the backward direction of weak measurement formalism. Our protocol works rigorously with the arbitrary measurement strength, which offers improved accuracy and precision. The precision can be further improved by taking into account the completeness condition of the measurement operators, which also ensures the feasibility of our protocol for the characterization of the arbitrary quantum measurement. Our work provides new insight on the symmetry between quantum states and measurements, as well as an efficient method to characterize a measurement apparatus.
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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
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Huichao 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
- Purple Mountain Laboratories, Nanjing, Jiangsu 211111, China
| | - Tao Jiang
- 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
| | - Feixiang 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
| | - Kaimin Zheng
- 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
| | - Ben Wang
- 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
| | - Aonan 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
| | - 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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15
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Zhou Y, Zhao J, Hay D, McGonagle K, Boyd RW, Shi Z. Direct Tomography of High-Dimensional Density Matrices for General Quantum States of Photons. PHYSICAL REVIEW LETTERS 2021; 127:040402. [PMID: 34355938 DOI: 10.1103/physrevlett.127.040402] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Revised: 06/21/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
Quantum-state tomography is the conventional method used to characterize density matrices for general quantum states. However, the data acquisition time generally scales linearly with the dimension of the Hilbert space, hindering the possibility of dynamic monitoring of a high-dimensional quantum system. Here, we demonstrate a direct tomography protocol to measure density matrices of photons in the position basis through the use of a polarization-resolving camera, where the dimension of density matrices can be as large as 580×580 in our experiment. The use of the polarization-resolving camera enables parallel measurements in the position and polarization basis and as a result, the data acquisition time of our protocol does not increase with the dimension of the Hilbert space and is solely determined by the camera exposure time (on the order of 10 ms). Our method is potentially useful for the real-time monitoring of the dynamics of quantum states and paves the way for the development of high-dimensional, time-efficient quantum metrology techniques.
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Affiliation(s)
- Yiyu Zhou
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Jiapeng Zhao
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Darrick Hay
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Kendrick McGonagle
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Robert W Boyd
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Zhimin Shi
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
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16
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Chen MC, Li Y, Liu RZ, Wu D, Su ZE, Wang XL, Li L, Liu NL, Lu CY, Pan JW. Directly Measuring a Multiparticle Quantum Wave Function via Quantum Teleportation. PHYSICAL REVIEW LETTERS 2021; 127:030402. [PMID: 34328769 DOI: 10.1103/physrevlett.127.030402] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
We propose a new method to directly measure a general multiparticle quantum wave function, a single matrix element in a multi-particle density matrix, by quantum teleportation. The density matrix element is embedded in a virtual logical qubit and is nondestructively teleported to a single physical qubit for readout. We experimentally implement this method to directly measure the wave function of a photonic mixed quantum state beyond a single photon using a single observable for the first time. Our method also provides an exponential advantage over the standard quantum state tomography in measurement complexity to fully characterize a sparse multiparticle quantum state.
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Affiliation(s)
- Ming-Cheng Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yuan Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Run-Ze Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Dian Wu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zu-En Su
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xi-Lin Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Nai-Le Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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17
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Ogawa K, Okazaki T, Kobayashi H, Nakanishi T, Tomita A. Direct measurement of ultrafast temporal wavefunctions. OPTICS EXPRESS 2021; 29:19403-19416. [PMID: 34266050 DOI: 10.1364/oe.423969] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 05/30/2021] [Indexed: 06/13/2023]
Abstract
The large capacity and robustness of information encoding in the temporal mode of photons is important in quantum information processing, in which characterizing temporal quantum states with high usability and time resolution is essential. We propose and demonstrate a direct measurement method of temporal complex wavefunctions for weak light at a single-photon level with subpicosecond time resolution. Our direct measurement is realized by ultrafast metrology of the interference between the light under test and self-generated monochromatic reference light; no external reference light or complicated post-processing algorithms are required. Hence, this method is versatile and potentially widely applicable for temporal state characterization.
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18
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Sahoo SN, Chakraborti S, Pati AK, Sinha U. Quantum State Interferography. PHYSICAL REVIEW LETTERS 2020; 125:123601. [PMID: 33016750 DOI: 10.1103/physrevlett.125.123601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Accepted: 08/11/2020] [Indexed: 06/11/2023]
Abstract
Quantum state tomography (QST) has been the traditional method for characterization of an unknown state. Recently, many direct measurement methods have been implemented to reconstruct the state in a resource efficient way. In this Letter, we present an interferometric method, in which any qubit state, whether mixed or pure, can be inferred from the visibility, phase shift, and average intensity of an interference pattern using a single-shot measurement-hence, we call it quantum state interferography. This provides us with a "black box" approach to quantum state estimation, wherein, between the incidence of the photon and extraction of state information, we are not changing any conditions within the setup, thus giving us a true single shot estimation of the quantum state. In contrast, standard QST requires at least two measurements for pure state qubit and at least three measurements for mixed state qubit reconstruction. We then go on to show that QSI is more resource efficient than QST for quantification of entanglement in pure bipartite qubits. We experimentally implement our method with high fidelity using the polarization degree of freedom of light. An extension of the scheme to pure states involving d-1 interferograms for d-dimensional systems is also presented. Thus, the scaling gain is even more dramatic in the qudit scenario for our method, where, in contrast, standard QST, without any assumptions, scales roughly as d^{2}.
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Affiliation(s)
| | | | - Arun K Pati
- Quantum Information and Computation Group, Harish-Chandra Research Institute, HBNI, Allahabad 211019, India
| | - Urbasi Sinha
- Light and Matter Physics, Raman Research Institute, Bengaluru 560080, India
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19
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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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20
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Ho LB. Systematic errors in direct state measurements with quantum controlled measurements. JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS 2020; 53:115501. [DOI: 10.1088/1361-6455/ab7881] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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21
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Hofmann HF. What Does the Operator Algebra of Quantum Statistics Tell Us about the Objective Causes of Observable Effects? ENTROPY 2020; 22:e22060638. [PMID: 33286410 PMCID: PMC7517172 DOI: 10.3390/e22060638] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Revised: 06/02/2020] [Accepted: 06/07/2020] [Indexed: 11/16/2022]
Abstract
Quantum physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a subjective lack of information regarding the physical reality of the system. In the present paper, I explore how the operator formalism accommodates the vast number of possible states and measurements by characterizing its essential function as a description of causality relations between initial conditions and subsequent observations. It is shown that any complete description of causality must involve non-positive statistical elements that cannot be associated with any directly observable effects. The necessity of non-positive elements is demonstrated by the uniquely defined mathematical description of ideal correlations which explains the physics of maximally entangled states, quantum teleportation and quantum cloning. The operator formalism thus modifies the concept of causality by providing a universally valid description of deterministic relations between initial states and subsequent observations that cannot be expressed in terms of directly observable measurement outcomes. Instead, the identifiable elements of causality are necessarily non-positive and hence unobservable. The validity of the operator algebra therefore indicates that a consistent explanation of the various uncertainty limited phenomena associated with physical objects is only possible if we learn to accept the fact that the elements of causality cannot be reconciled with a continuation of observable reality in the physical object.
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Affiliation(s)
- Holger F Hofmann
- Graduate School of Advanced Science and Engineering, Hiroshima University, Kagamiyama 1-3-1, Higashi Hiroshima 739-8530, Japan
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22
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Xin M, Zeng L, Ran D, Chen X, Xu Y, Shi D, He Y, Zhong S. Label-free rapid identification of cooked meat using MIP-quantum weak measurement. FOOD AGR IMMUNOL 2020. [DOI: 10.1080/09540105.2020.1726879] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Meiguo Xin
- Department of Food Science and Technology, Foshan University, Guangdong, People’s Republic of China
| | - Lin Zeng
- Department of Food Science and Technology, Foshan University, Guangdong, People’s Republic of China
| | - Di Ran
- Department of Food Science and Technology, Foshan University, Guangdong, People’s Republic of China
| | - Xiangmei Chen
- Department of Food Science and Technology, Foshan University, Guangdong, People’s Republic of China
| | - Yang Xu
- Institute of Optical Imaging and Sensing, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People’s Republic of China
| | - Daoxuan Shi
- Institute of Optical Imaging and Sensing, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People’s Republic of China
| | - Yonghong He
- Institute of Optical Imaging and Sensing, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People’s Republic of China
| | - Suyi Zhong
- Institute of Optical Imaging and Sensing, Graduate School at Shenzhen, Tsinghua University, Shenzhen, People’s Republic of China
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23
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Zhang S, Zhou Y, Mei Y, Liao K, Wen YL, Li J, Zhang XD, Du S, Yan H, Zhu SL. δ-Quench Measurement of a Pure Quantum-State Wave Function. PHYSICAL REVIEW LETTERS 2019; 123:190402. [PMID: 31765181 DOI: 10.1103/physrevlett.123.190402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Indexed: 06/10/2023]
Abstract
The measurement of a quantum state wave function not only acts as a fundamental part in quantum physics but also plays an important role in developing practical quantum technologies. Conventional quantum state tomography has been widely used to estimate quantum wave functions, which usually requires complicated measurement techniques. The recent weak-value-based quantum measurement circumvents this resource issue but relies on an extra pointer space. Here, we theoretically propose and then experimentally demonstrate a direct and efficient measurement strategy based on a δ-quench probe: by quenching its complex probability amplitude one by one (δ quench) in the given basis, we can directly obtain the quantum wave function of a pure ensemble by projecting the quenched state onto a postselection state. We confirm its power by experimentally measuring photonic complex temporal wave functions. This new method is versatile and can find applications in quantum information science and engineering.
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Affiliation(s)
- Shanchao Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yiru Zhou
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yefeng Mei
- Department of Physics & William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong S.A.R., China
| | - Kaiyu Liao
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yong-Li Wen
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Jianfeng Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Xin-Ding Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Shengwang Du
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
- Department of Physics & William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong S.A.R., China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
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24
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Pan WW, Xu XY, Kedem Y, Wang QQ, Chen Z, Jan M, Sun K, Xu JS, Han YJ, Li CF, Guo GC. Direct Measurement of a Nonlocal Entangled Quantum State. PHYSICAL REVIEW LETTERS 2019; 123:150402. [PMID: 31702297 DOI: 10.1103/physrevlett.123.150402] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Revised: 06/24/2019] [Indexed: 06/10/2023]
Abstract
Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen et al. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.
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Affiliation(s)
- Wei-Wei Pan
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Yaron Kedem
- Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
| | - Qin-Qin Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zhe Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Munsif Jan
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Kai Sun
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Yong-Jian Han
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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25
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Zhang YJ, Shi LX, Xu Y, Zheng X, Li JW, Wu Q, Li SX, He YH. Optical quantum weak measurement coupled with UV spectrophotometry for sensitively and non-separatedly detecting enantiopurity. OPTICS EXPRESS 2019; 27:9330-9342. [PMID: 31045086 DOI: 10.1364/oe.27.009330] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2018] [Accepted: 03/06/2019] [Indexed: 06/09/2023]
Abstract
Based on the theories of quantum weak measurement, we built a set of linear common-path optical weak measurement systems in frequency domain for detecting chiral molecules. The polarization resolution with this system to detect the optical rotation of chirality molecules is nearly two orders of magnitude higher than that of conventional polarizers. Combined with ultraviolet spectroscopy, the purity of the proline enantiomers mixture was detected. The purity resolution can reach to 0.14%, which is comparable to the liquid chromatography. Weak measurement combined with ultraviolet spectroscopy to non-separatedly detect the purity of chiral enantiomers has great application potential in the pharmaceutical industry.
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26
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Chen JS, Hu MJ, Hu XM, Liu BH, Huang YF, Li CF, Guo CG, Zhang YS. Experimental realization of sequential weak measurements of non-commuting Pauli observables. OPTICS EXPRESS 2019; 27:6089-6097. [PMID: 30876202 DOI: 10.1364/oe.27.006089] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2018] [Accepted: 01/13/2019] [Indexed: 06/09/2023]
Abstract
Sequential weak measurements of non-commuting observables are not only fundamentally interesting in terms of quantum measurement but also show potential in various applications. Previously reported methods, however, can only make limited sequential weak measurements experimentally. In this article, we propose the realization of sequential measurements of non-commuting Pauli observables and experimentally demonstrate for the first time the measurement of sequential weak values of three non-commuting Pauli observables using genuine single photons.
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27
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Ho LB. Improving direct state measurements by using rebits in real enlarged Hilbert spaces. PHYSICS LETTERS A 2019; 383:289-294. [DOI: 10.1016/j.physleta.2018.10.047] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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28
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Calderaro L, Foletto G, Dequal D, Villoresi P, Vallone G. Direct Reconstruction of the Quantum Density Matrix by Strong Measurements. PHYSICAL REVIEW LETTERS 2018; 121:230501. [PMID: 30576212 DOI: 10.1103/physrevlett.121.230501] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Indexed: 06/09/2023]
Abstract
New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only O(d) different operations, compared to d^{2} linearly independent projectors in the case of standard quantum state tomography, for the reconstruction of an arbitrary mixed state. However, due to the weakness of these couplings, these protocols are approximated and prone to large statistical errors. We propose a method which is similar to the weak measurement protocols but works regardless of the coupling strength: our protocol is not approximated and thus improves the accuracy and precision of the results with respect to weak measurement schemes. We experimentally apply it to the polarization state of single photons and compare the results to those of preexisting methods for different values of the coupling strength. Our results show that our method outperforms previous proposals in terms of accuracy and statistical errors.
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Affiliation(s)
- Luca Calderaro
- Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo 6B, 35131 Padova, Italy
- Centro di Ateneo di Studi e Attività Spaziali "Giuseppe Colombo", Università di Padova, via Venezia 15, 35131 Padova, Italy
| | - Giulio Foletto
- Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo 6B, 35131 Padova, Italy
| | - Daniele Dequal
- Matera Laser Ranging Observatory, Agenzia Spaziale Italiana, Matera 75100, Italy
| | - Paolo Villoresi
- Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo 6B, 35131 Padova, Italy
- Istituto di Fotonica e Nanotecnologie, CNR, via Trasea 7, 35131 Padova, Italy
| | - Giuseppe Vallone
- Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo 6B, 35131 Padova, Italy
- Istituto di Fotonica e Nanotecnologie, CNR, via Trasea 7, 35131 Padova, Italy
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29
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An XB, Li HW, Yin ZQ, Hu MJ, Huang W, Xu BJ, Wang S, Chen W, Guo GC, Han ZF. Experimental three-party quantum random number generator based on dimension witness violation and weak measurement. OPTICS LETTERS 2018; 43:3437-3440. [PMID: 30004524 DOI: 10.1364/ol.43.003437] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2018] [Accepted: 06/13/2018] [Indexed: 06/08/2023]
Abstract
Random number generation is an important task in modern science. A variety of quantum random number generation protocols have been proposed and realized. These protocols, however, are all based on two parties. Based on the weak measurement technique, we propose and realize a quantum random number generator among three observers. The violation of a double classical dimension witness based on the determinant value is first observed in experiment. With the heralding single-photon source, our experimental setup attains the independent assumption and the dimension assumption, which means our setup is semi-device-independent (DI). This Letter sheds new light on generating DI-type random number among multi-user and it has potential application prospect on the quantum cryptography and quantum random number in network environment.
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30
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Qin L, Wang Z, Zhang C, Li XQ. Direct measurement of the quantum state of photons in a cavity. OPTICS EXPRESS 2018; 26:7034-7042. [PMID: 29609389 DOI: 10.1364/oe.26.007034] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Accepted: 12/18/2017] [Indexed: 06/08/2023]
Abstract
We propose a scheme to measure the quantum state of photons in a cavity. The proposal is based on the concept of quantum weak values and applies equally well to both the solid-state circuit and atomic cavity quantum electrodynamics (QED) systems. The proposed scheme allows us to access directly the superposition components in Fock state basis, rather than the Wigner function as usual in phase space. Moreover, the separate access feature held in the direct scheme does not require a global reconstruction for the quantum state, which provides a particular advantage beyond the conventional method of quantum state tomography.
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31
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Miller HJD, Anders J. Leggett-Garg Inequalities for Quantum Fluctuating Work. ENTROPY (BASEL, SWITZERLAND) 2018; 20:E200. [PMID: 33265291 PMCID: PMC7845770 DOI: 10.3390/e20030200] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2018] [Revised: 02/28/2018] [Accepted: 03/08/2018] [Indexed: 11/16/2022]
Abstract
The Leggett-Garg inequalities serve to test whether or not quantum correlations in time can be explained within a classical macrorealistic framework. We apply this test to thermodynamics and derive a set of Leggett-Garg inequalities for the statistics of fluctuating work done on a quantum system unitarily driven in time. It is shown that these inequalities can be violated in a driven two-level system, thereby demonstrating that there exists no general macrorealistic description of quantum work. These violations are shown to emerge within the standard Two-Projective-Measurement scheme as well as for alternative definitions of fluctuating work that are based on weak measurement. Our results elucidate the influences of temporal correlations on work extraction in the quantum regime and highlight a key difference between quantum and classical thermodynamics.
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Affiliation(s)
| | - Janet Anders
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
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32
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Direct quantum process tomography via measuring sequential weak values of incompatible observables. Nat Commun 2018; 9:192. [PMID: 29335489 PMCID: PMC5768737 DOI: 10.1038/s41467-017-02511-2] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2017] [Accepted: 12/06/2017] [Indexed: 11/09/2022] Open
Abstract
The weak value concept has enabled fundamental studies of quantum measurement and, recently, found potential applications in quantum and classical metrology. However, most weak value experiments reported to date do not require quantum mechanical descriptions, as they only exploit the classical wave nature of the physical systems. In this work, we demonstrate measurement of the sequential weak value of two incompatible observables by making use of two-photon quantum interference so that the results can only be explained quantum physically. We then demonstrate that the sequential weak value measurement can be used to perform direct quantum process tomography of a qubit channel. Our work not only demonstrates the quantum nature of weak values but also presents potential new applications of weak values in analyzing quantum channels and operations.
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33
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Zhou ZY, Zhu ZH, Liu SL, Li YH, Shi S, Ding DS, Chen LX, Gao W, Guo GC, Shi BS. Quantum twisted double-slits experiments: confirming wavefunctions' physical reality. Sci Bull (Beijing) 2017; 62:1185-1192. [PMID: 36659512 DOI: 10.1016/j.scib.2017.08.024] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2017] [Revised: 08/19/2017] [Accepted: 08/21/2017] [Indexed: 01/21/2023]
Abstract
Are quantum states real? This most fundamental question in quantum mechanics has not yet been satisfactorily resolved, although its realistic interpretation seems to have been rejected by various delayed-choice experiments. Here, to address this long-standing issue, we present a quantum twisted double-slit experiment. By exploiting the subluminal feature of twisted photons, the real nature of a photon during its time in flight is revealed for the first time. We found that photons' arrival times were inconsistent with the states obtained in measurements but agreed with the states during propagation. Our results demonstrate that wavefunctions describe the realistic existence and evolution of quantum entities rather than a pure mathematical abstraction providing a probability list of measurement outcomes. This finding clarifies the long-held misunderstanding of the role of wavefunctions and their collapse in the evolution of quantum entities.
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Affiliation(s)
- Zhi-Yuan Zhou
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Zhi-Han Zhu
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; Department of Physics, Harbin University of Science and Technology, Harbin 150080, China.
| | - Shi-Long Liu
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Yin-Hai Li
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Shuai Shi
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Dong-Sheng Ding
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Li-Xiang Chen
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; Department of Physics and Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices, Xiamen University, Xiamen 361005, China
| | - Wei Gao
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; Department of Physics, Harbin University of Science and Technology, Harbin 150080, China
| | - Guang-Can Guo
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Bao-Sen Shi
- Wang Da-Heng Collaborative Innovation Center for Science of Quantum Manipulation & Control, Heilongjiang Province & Harbin University of Science and Technology, Harbin 150080, China; CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China.
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34
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Using coherence to enhance function in chemical and biophysical systems. Nature 2017; 543:647-656. [DOI: 10.1038/nature21425] [Citation(s) in RCA: 398] [Impact Index Per Article: 56.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2016] [Accepted: 12/07/2016] [Indexed: 12/23/2022]
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35
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Piacentini F, Avella A, Levi MP, Gramegna M, Brida G, Degiovanni IP, Cohen E, Lussana R, Villa F, Tosi A, Zappa F, Genovese M. Measuring Incompatible Observables by Exploiting Sequential Weak Values. PHYSICAL REVIEW LETTERS 2016; 117:170402. [PMID: 27824450 DOI: 10.1103/physrevlett.117.170402] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Indexed: 06/06/2023]
Abstract
One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.
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Affiliation(s)
- F Piacentini
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - A Avella
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - M P Levi
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - M Gramegna
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - G Brida
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | | | - E Cohen
- Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - R Lussana
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - F Villa
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - A Tosi
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - F Zappa
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - M Genovese
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy and INFN, Via P. Giuria 1, I-10125 Torino, Italy
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36
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Thekkadath GS, Giner L, Chalich Y, Horton MJ, Banker J, Lundeen JS. Direct Measurement of the Density Matrix of a Quantum System. PHYSICAL REVIEW LETTERS 2016; 117:120401. [PMID: 27689255 DOI: 10.1103/physrevlett.117.120401] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Indexed: 06/06/2023]
Abstract
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
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Affiliation(s)
- G S Thekkadath
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - L Giner
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - Y Chalich
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - M J Horton
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - J Banker
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - J S Lundeen
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
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37
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Marian D, Zanghì N, Oriols X. Weak Values from Displacement Currents in Multiterminal Electron Devices. PHYSICAL REVIEW LETTERS 2016; 116:110404. [PMID: 27035291 DOI: 10.1103/physrevlett.116.110404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2015] [Indexed: 06/05/2023]
Abstract
Weak values allow the measurement of observables associated with noncommuting operators. Up to now, position-momentum weak values have been mainly developed for (relativistic) photons. In this Letter, a proposal for the measurement of such weak values in typical electronic devices is presented. Inspired by the Ramo-Shockley-Pellegrini theorem that provides a relation between current and electron velocity, it is shown that the displacement current measured in multiterminal configurations can provide either a weak measurement of the momentum or strong measurement of position. This proposal opens new opportunities for fundamental and applied physics with state-of-the-art electronic technology. As an example, a setup for the measurement of the Bohmian velocity of (nonrelativistic) electrons is presented and tested with numerical experiments.
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Affiliation(s)
- D Marian
- Dipartimento di Fisica dell'Università di Genova and INFN sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
- Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193-Bellaterra (Barcelona), Spain
| | - N Zanghì
- Dipartimento di Fisica dell'Università di Genova and INFN sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
| | - X Oriols
- Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193-Bellaterra (Barcelona), Spain
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38
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Vallone G, Dequal D. Strong Measurements Give a Better Direct Measurement of the Quantum Wave Function. PHYSICAL REVIEW LETTERS 2016; 116:040502. [PMID: 26871315 DOI: 10.1103/physrevlett.116.040502] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2015] [Indexed: 06/05/2023]
Abstract
Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wave function [4J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e., those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.
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Affiliation(s)
- Giuseppe Vallone
- Department of Information Engineering, University of Padova, via Gradenigo 6/B, 35131 Padova, Italy
| | - Daniele Dequal
- Department of Information Engineering, University of Padova, via Gradenigo 6/B, 35131 Padova, Italy
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39
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Bartkiewicz K, Černoch A, Lemr K, Miranowicz A. Priority Choice Experimental Two-Qubit Tomography: Measuring One by One All Elements of Density Matrices. Sci Rep 2016; 6:19610. [PMID: 26792194 PMCID: PMC4726363 DOI: 10.1038/srep19610] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2015] [Accepted: 12/11/2015] [Indexed: 11/09/2022] Open
Abstract
In standard optical tomographic methods, the off-diagonal elements of a density matrix ρ are measured indirectly. Thus, the reconstruction of ρ, even if it is based on linear inversion, typically magnifies small errors in the experimental data. Recently, an optimal tomography solution measuring all the elements of ρ one-by-one without error magnification has been theoretically proposed. We implemented this method for two-qubit polarization states. For comparison, we also experimentally implemented other well-known tomographic protocols, either based solely on local measurements (of, e.g., the Pauli operators and James-Kwiat-Munro-White projectors) or with mutually unbiased bases requiring both local and global measurements. We reconstructed seventeen separable, partially and maximally entangled two-qubit polarization states. Our experiments show that our method has the highest stability against errors in comparison to other quantum tomographies. In particular, we demonstrate that each optimally-reconstructed state is embedded in an uncertainty circle of the smallest radius, both in terms of trace distance and disturbance. We explain how to experimentally estimate uncertainty radii for all the implemented tomographies and show that, for each reconstructed state, the relevant uncertainty circles intersect indicating the approximate location of the corresponding physical density matrix.
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Affiliation(s)
- Karol Bartkiewicz
- Faculty of Physics, Adam Mickiewicz University, PL-61-614 Poznań, Poland.,RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Academy of Sciences of the Czech Republic, 17. listopadu 12, 772 07 Olomouc, Czech Republic
| | - Antonín Černoch
- Institute of Physics of Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of Palacký University and Institute of Physics of Academy of Sciences of the Czech Republic, 17. listopadu 50A, 77207 Olomouc, Czech Republic
| | - Karel Lemr
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Academy of Sciences of the Czech Republic, 17. listopadu 12, 772 07 Olomouc, Czech Republic
| | - Adam Miranowicz
- Faculty of Physics, Adam Mickiewicz University, PL-61-614 Poznań, Poland.,CEMS, RIKEN, 351-0198 Wako-shi, Japan
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40
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Zhang L, Datta A, Walmsley IA. Precision metrology using weak measurements. PHYSICAL REVIEW LETTERS 2015; 114:210801. [PMID: 26066422 DOI: 10.1103/physrevlett.114.210801] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2013] [Indexed: 06/04/2023]
Abstract
Weak values and measurements have been proposed as a means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology. Namely, (Q1) Does postselection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyze these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.
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Affiliation(s)
- Lijian Zhang
- National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Max Planck Institute for Structure and Dynamics of Material, Hamburg 22761, Germany
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
- Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Ian A Walmsley
- Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
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41
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Dressel J, Bliokh KY, Nori F. Classical field approach to quantum weak measurements. PHYSICAL REVIEW LETTERS 2014; 112:110407. [PMID: 24702338 DOI: 10.1103/physrevlett.112.110407] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2013] [Indexed: 06/03/2023]
Abstract
By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and postselected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.
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Affiliation(s)
- Justin Dressel
- Center for Emergent Matter Science, RIKEN, Saitama 351-0198, Japan
| | - Konstantin Y Bliokh
- Interdisciplinary Theoretical Science Research Group, RIKEN, Saitama 351-0198, Japan
| | - Franco Nori
- Center for Emergent Matter Science, RIKEN, Saitama 351-0198, Japan and Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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42
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Bamber C, Lundeen JS. Observing Dirac's classical phase space analog to the quantum state. PHYSICAL REVIEW LETTERS 2014; 112:070405. [PMID: 24579574 DOI: 10.1103/physrevlett.112.070405] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2013] [Indexed: 06/03/2023]
Abstract
In 1945, Dirac attempted to develop a “formal probability” distribution to describe quantum operators in terms of two noncommuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting quasiprobability distribution is a complete representation of the quantum state and can be observed directly in experiments. We measure Dirac’s distribution for the quantum state of the transverse degree of freedom of a photon by weakly measuring transverse x so as to not randomize the subsequent p measurement. Furthermore, we show that the distribution has the classical-like feature that it transforms (e.g., propagates) according to Bayes’ law.
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Affiliation(s)
- Charles Bamber
- Measurement Science and Standards, National Research Council, Ottawa, Canada K1A 0R6
| | - Jeff S Lundeen
- Physics Department, University of Ottawa, 150 Louis Pasteur, Ottawa, Canada K1N 6N5
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43
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Direct measurement of a 27-dimensional orbital-angular-momentum state vector. Nat Commun 2014; 5:3115. [DOI: 10.1038/ncomms4115] [Citation(s) in RCA: 165] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2013] [Accepted: 12/16/2013] [Indexed: 11/09/2022] Open
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44
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Qi B, Hou Z, Li L, Dong D, Xiang G, Guo G. Quantum state tomography via linear regression estimation. Sci Rep 2013; 3:3496. [PMID: 24336519 PMCID: PMC3861803 DOI: 10.1038/srep03496] [Citation(s) in RCA: 79] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2013] [Accepted: 11/28/2013] [Indexed: 11/18/2022] Open
Abstract
A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography.
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Affiliation(s)
- Bo Qi
- Key Laboratory of Systems and Control, ISS, and National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, CAS, Beijing 100190, P. R. China
| | - Zhibo Hou
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, P. R. China
| | - Li Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, P. R. China
| | - Daoyi Dong
- School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia
| | - Guoyong Xiang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, P. R. China
| | - Guangcan Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, P. R. China
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45
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Shomroni I, Bechler O, Rosenblum S, Dayan B. Demonstration of weak measurement based on atomic spontaneous emission. PHYSICAL REVIEW LETTERS 2013; 111:023604. [PMID: 23889401 DOI: 10.1103/physrevlett.111.023604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2012] [Indexed: 06/02/2023]
Abstract
We demonstrate a new type of weak measurement based on the dynamics of spontaneous emission. The pointer in our scheme is given by the Lorentzian distribution characterizing atomic exponential decay via emission of a single photon. We thus introduce weak measurement, so far demonstrated nearly exclusively with laser beams and Gaussian statistics, into the quantum regime of single emitters and single quanta, enabling the exploitation of a wide class of sources that are abundant in nature. We describe a complete analogy between our scheme and weak measurement with conventional Gaussian pointers. Instead of a shift in the mean of a Gaussian distribution, an imaginary weak value is exhibited in our scheme by a significantly slower-than-natural exponential distribution of emitted photons at the postselected polarization, leading to a large shift in their mean arrival time. The dynamics of spontaneous emission offer a broader view of the measurement process than is usually considered within the weak measurement formalism. Our scheme opens the path for the use of atoms and atomlike systems as sensitive probes in weak measurements, one example being optical magnetometry.
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Affiliation(s)
- Itay Shomroni
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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46
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Abstract
Recent work has revealed that the wave function of a pure state can be measured directly and that complementary knowledge of a quantum system can be obtained simultaneously by weak measurements. However, the original scheme applies only to pure states, and it is not efficient because most of the data are discarded by post-selection. Here, we propose tomography schemes for pure states and for mixed states via weak measurements, and our schemes are more efficient because we do not discard any data. Furthermore, we demonstrate that any matrix element of a general state can be directly read from an appropriate weak measurement. The density matrix (with all of its elements) represents all that is directly accessible from a general measurement.
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Affiliation(s)
- Shengjun Wu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
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47
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Di Lorenzo A. Sequential measurement of conjugate variables as an alternative quantum state tomography. PHYSICAL REVIEW LETTERS 2013; 110:010404. [PMID: 23383764 DOI: 10.1103/physrevlett.110.010404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2012] [Indexed: 06/01/2023]
Abstract
It is shown how it is possible to reconstruct the initial state of a one-dimensional system by sequentially measuring two conjugate variables. The procedure relies on the quasicharacteristic function, the Fourier transform of the Wigner quasiprobability. The proper characteristic function obtained by Fourier transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasicharacteristic function of the two detectors and that unknown of the quantum system. This allows state reconstruction through the sequence (1) data collection, (2) Fourier transform, (3) algebraic operation, and (4) inverse Fourier transform. The strength of the measurement should be intermediate for the procedure to work.
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Affiliation(s)
- Antonio Di Lorenzo
- Instituto de Física, Universidade Federal de Uberlândia, 38400-902 Uberlândia, Minas Gerais, Brazil
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Hofmann HF. How weak values emerge in joint measurements on cloned quantum systems. PHYSICAL REVIEW LETTERS 2012; 109:020408. [PMID: 23030138 DOI: 10.1103/physrevlett.109.020408] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2011] [Indexed: 06/01/2023]
Abstract
A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but nonpositive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems, resulting in perfect correlations for all observables. The joint probabilities for noncommuting measurements on separate clones then correspond to the real parts of the complex joint probabilities observed in weak measurements on a single system, where the measurements on the two clones replace the corresponding sequence of weak measurement and postselection. The imaginary parts of weak measurement statics can be obtained by replacing the cloning process with a partial swap operation. A controlled-swap operation combines both processes, making the complete weak measurement statistics accessible as a well-defined contribution to the joint probabilities of fully resolved projective measurements on the two output systems.
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Affiliation(s)
- Holger F Hofmann
- Graduate School of Advanced Sciences of Matter, Hiroshima University, Kagamiyama 1-3-1, Higashi Hiroshima 739-8530, Japan.
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