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Song X, Salvati F, Gaikwad C, Yunger Halpern N, Arvidsson-Shukur DRM, Murch K. Agnostic Phase Estimation. PHYSICAL REVIEW LETTERS 2024; 132:260801. [PMID: 38996278 DOI: 10.1103/physrevlett.132.260801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Accepted: 05/13/2024] [Indexed: 07/14/2024]
Abstract
The goal of quantum metrology is to improve measurements' sensitivities by harnessing quantum resources. Metrologists often aim to maximize the quantum Fisher information, which bounds the measurement setup's sensitivity. In studies of fundamental limits on metrology, a paradigmatic setup features a qubit (spin-half system) subject to an unknown rotation. One obtains the maximal quantum Fisher information about the rotation if the spin begins in a state that maximizes the variance of the rotation-inducing operator. If the rotation axis is unknown, however, no optimal single-qubit sensor can be prepared. Inspired by simulations of closed timelike curves, we circumvent this limitation. We obtain the maximum quantum Fisher information about a rotation angle, regardless of the unknown rotation axis. To achieve this result, we initially entangle the probe qubit with an ancilla qubit. Then, we measure the pair in an entangled basis, obtaining more information about the rotation angle than any single-qubit sensor can achieve. We demonstrate this metrological advantage using a two-qubit superconducting quantum processor. Our measurement approach achieves a quantum advantage, outperforming every entanglement-free strategy.
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Yang J. Theory of Compression Channels for Postselected Quantum Metrology. PHYSICAL REVIEW LETTERS 2024; 132:250802. [PMID: 38996257 DOI: 10.1103/physrevlett.132.250802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Accepted: 05/20/2024] [Indexed: 07/14/2024]
Abstract
The postselected quantum metrological scheme is especially advantageous when the final measurements are either very noisy or expensive in practical experiments. In this Letter, we put forward a general theory on the compression channels in postselected quantum metrology. We define the basic notions characterizing the compression quality and illuminate the underlying structure of lossless compression channels. Previous experiments on postselected optical phase estimation and weak-value amplification are shown to be particular cases of this general theory. Furthermore, for two categories of bipartite systems, we show that the compression loss can be made arbitrarily small even when the compression channel acts only on one subsystem. These findings can be employed to distribute quantum measurements so that the measurement noise and cost are dramatically reduced.
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Arvidsson-Shukur DRM, McConnell AG, Yunger Halpern N. Nonclassical Advantage in Metrology Established via Quantum Simulations of Hypothetical Closed Timelike Curves. PHYSICAL REVIEW LETTERS 2023; 131:150202. [PMID: 37897785 DOI: 10.1103/physrevlett.131.150202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2022] [Revised: 09/08/2023] [Accepted: 09/11/2023] [Indexed: 10/30/2023]
Abstract
We construct a metrology experiment in which the metrologist can sometimes amend the input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change the input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist's winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.
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Affiliation(s)
| | - Aidan G McConnell
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
- Laboratory for X-ray Nanoscience and Technologies, Paul Scherrer Institut, 5232 Villigen, Switzerland
- Department of Physics and Quantum Center, Eidgenössische Technische Hochschule Zürich, CH-8093 Zürich, Switzerland
| | - Nicole Yunger Halpern
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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4
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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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5
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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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Rizvi SMA, Asif N, Ulum MS, Duong TQ, Shin H. Multiclass Classification of Metrologically Resourceful Tripartite Quantum States with Deep Neural Networks. SENSORS (BASEL, SWITZERLAND) 2022; 22:6767. [PMID: 36146114 PMCID: PMC9500965 DOI: 10.3390/s22186767] [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: 07/14/2022] [Revised: 08/24/2022] [Accepted: 09/04/2022] [Indexed: 06/16/2023]
Abstract
Quantum entanglement is a unique phenomenon of quantum mechanics, which has no classical counterpart and gives quantum systems their advantage in computing, communication, sensing, and metrology. In quantum sensing and metrology, utilizing an entangled probe state enhances the achievable precision more than its classical counterpart. Noise in the probe state preparation step can cause the system to output unentangled states, which might not be resourceful. Hence, an effective method for the detection and classification of tripartite entanglement is required at that step. However, current mathematical methods cannot robustly classify multiclass entanglement in tripartite quantum systems, especially in the case of mixed states. In this paper, we explore the utility of artificial neural networks for classifying the entanglement of tripartite quantum states into fully separable, biseparable, and fully entangled states. We employed Bell's inequality for the dataset of tripartite quantum states and train the deep neural network for multiclass classification. This entanglement classification method is computationally efficient due to using a small number of measurements. At the same time, it also maintains generalization by covering a large Hilbert space of tripartite quantum states.
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Affiliation(s)
- Syed Muhammad Abuzar Rizvi
- Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin 17104, Korea
| | - Naema Asif
- Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin 17104, Korea
| | - Muhammad Shohibul Ulum
- Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin 17104, Korea
| | - Trung Q. Duong
- School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast BT7 1NN, UK
| | - Hyundong Shin
- Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin 17104, Korea
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7
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Symmetries of Quantum Fisher Information as Parameter Estimator for Pauli Channels under Indefinite Causal Order. Symmetry (Basel) 2022. [DOI: 10.3390/sym14091813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Quantum Fisher Information is considered in Quantum Information literature as the main resource to determine a bound in the parametric characterization problem of a quantum channel by means of probe states. The parameters characterizing a quantum channel can be estimated until a limited precision settled by the Cramér–Rao bound established in estimation theory and statistics. The involved Quantum Fisher Information of the emerging quantum state provides such a bound. Quantum states with dimension d=2, the qubits, still comprise the main resources considered in Quantum Information and Quantum Processing theories. For them, Pauli channels are an important family of parametric quantum channels providing the most faithful deformation effects of imperfect quantum communication channels. Recently, Pauli channels have been characterized when they are arranged in an Indefinite Causal Order. Thus, their fidelity has been compared with single or sequential arrangements of identical channels to analyse their induced transparency under a joint behaviour. The most recent characterization has exhibited important features for quantum communication related with their parametric nature. In this work, a parallel analysis has been conducted to extended such a characterization, this time in terms of their emerging Quantum Fisher Information to pursue the advantages of each kind of arrangement for the parameter estimation problem. The objective is to reach the arrangement stating the best estimation bound for each type of Pauli channel. A complete map for such an effectivity is provided for each Pauli channel under the most affordable setups considering sequential and Indefinite Causal Order arrangements, as well as discussing their advantages and disadvantages.
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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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Patil YSS, Yu J, Frazier S, Wang Y, Johnson K, Fox J, Reichel J, Harris JGE. Measuring High-Order Phonon Correlations in an Optomechanical Resonator. PHYSICAL REVIEW LETTERS 2022; 128:183601. [PMID: 35594119 DOI: 10.1103/physrevlett.128.183601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Accepted: 03/18/2022] [Indexed: 06/15/2023]
Abstract
We use single photon detectors to probe the motional state of a superfluid ^{4}He resonator of mass ∼1 ng. The arrival times of Stokes and anti-Stokes photons (scattered by the resonator's acoustic mode) are used to measure the resonator's phonon coherences up to the fourth order. By postselecting on photon detection events, we also measure coherences in the resonator when ≤3 phonons have been added or subtracted. These measurements are found to be consistent with predictions that assume the acoustic mode to be in thermal equilibrium with a bath through a Markovian coupling.
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Affiliation(s)
- Y S S Patil
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - J Yu
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S Frazier
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Y Wang
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - K Johnson
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - J Fox
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - J Reichel
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France 24 rue Lhomond, 75005 Paris, France
| | - J G E Harris
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA
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10
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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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11
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Monroe JT, Yunger Halpern N, Lee T, Murch KW. Weak Measurement of a Superconducting Qubit Reconciles Incompatible Operators. PHYSICAL REVIEW LETTERS 2021; 126:100403. [PMID: 33784149 DOI: 10.1103/physrevlett.126.100403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Revised: 11/19/2020] [Accepted: 01/29/2021] [Indexed: 06/12/2023]
Abstract
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state information without projection. Recently, weak measurements were shown to obey an uncertainty relation cast in terms of entropies. We experimentally test this entropic uncertainty relation with strong and weak measurements of a superconducting transmon qubit. A weak measurement, we find, can reconcile two strong measurements' incompatibility, via backaction on the state. Mathematically, a weak value-a preselected and postselected expectation value-lowers the uncertainty bound. Hence we provide experimental support for the physical interpretation of the weak value as a determinant of a weak measurement's ability to reconcile incompatible operations.
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Affiliation(s)
- Jonathan T Monroe
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Nicole Yunger Halpern
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- 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
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Taeho Lee
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Kater W Murch
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
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12
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Lostaglio M. Certifying Quantum Signatures in Thermodynamics and Metrology via Contextuality of Quantum Linear Response. PHYSICAL REVIEW LETTERS 2020; 125:230603. [PMID: 33337232 DOI: 10.1103/physrevlett.125.230603] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2020] [Accepted: 11/03/2020] [Indexed: 06/12/2023]
Abstract
I identify a fundamental difference between classical and quantum dynamics in the linear response regime by showing that the latter is, in general, contextual. This allows me to provide an example of a quantum engine whose favorable power output scaling unavoidably requires nonclassical effects in the form of contextuality. Furthermore, I describe contextual advantages for local metrology. Given the ubiquity of linear response theory, I anticipate that these tools will allow one to certify the nonclassicality of a wide array of quantum phenomena.
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Affiliation(s)
- Matteo Lostaglio
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
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Amaral B. Resource theory of contextuality. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20190010. [PMID: 31522637 PMCID: PMC6754716 DOI: 10.1098/rsta.2019.0010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/10/2019] [Indexed: 06/10/2023]
Abstract
In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental importance to study contextuality from the point of view of resource theories, which provide a powerful framework for the formal treatment of a property as an operational resource. In this contribution, we review recent developments towards a resource theory of contextuality and connections with operational applications of this property. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.
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Affiliation(s)
- Barbara Amaral
- Departamento de Física e Matemática, CAP - Universidade Federal de São João del-Rei, 36.420-000 Ouro Branco, MG, Brazil
- Department of Mathematical Physics, Institute of Physics, University of São Paulo, R. do Matao 1371, São Paulo 05508-090, SP, Brazil
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