1
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Wang QQ, Dong S, Li XW, Xu XY, Wang C, Han S, Yung MH, Han YJ, Li CF, Guo GC. Efficient learning of mixed-state tomography for photonic quantum walk. SCIENCE ADVANCES 2024; 10:eadl4871. [PMID: 38489356 DOI: 10.1126/sciadv.adl4871] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 02/11/2024] [Indexed: 03/17/2024]
Abstract
Noise-enhanced applications in open quantum walk (QW) has recently seen a surge due to their ability to improve performance. However, verifying the success of open QW is challenging, as mixed-state tomography is a resource-intensive process, and implementing all required measurements is almost impossible due to various physical constraints. To address this challenge, we present a neural-network-based method for reconstructing mixed states with a high fidelity (∼97.5%) while costing only 50% of the number of measurements typically required for open discrete-time QW in one dimension. Our method uses a neural density operator that models the system and environment, followed by a generalized natural gradient descent procedure that significantly speeds up the training process. Moreover, we introduce a compact interferometric measurement device, improving the scalability of our photonic QW setup that enables experimental learning of mixed states. Our results demonstrate that highly expressive neural networks can serve as powerful alternatives to traditional state tomography.
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Affiliation(s)
- Qin-Qin Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Shaojun Dong
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230031, China
| | - Xiao-Wei Li
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chao Wang
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230031, China
| | - Shuai Han
- Yangtze Delta Region Industrial Innovation Center of Quantum and Information Technology, Suzhou 215100, China
| | - Man-Hong Yung
- Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yong-Jian Han
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230031, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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2
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Morrigan L, Neville SP, Gregory M, Boguslavskiy AE, Forbes R, Wilkinson I, Lausten R, Stolow A, Schuurman MS, Hockett P, Makhija V. Ultrafast Molecular Frame Quantum Tomography. PHYSICAL REVIEW LETTERS 2023; 131:193001. [PMID: 38000424 DOI: 10.1103/physrevlett.131.193001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Revised: 09/05/2023] [Accepted: 10/03/2023] [Indexed: 11/26/2023]
Abstract
We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH_{3}). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH_{3}, we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.
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Affiliation(s)
- Luna Morrigan
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
| | - Simon P Neville
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Margaret Gregory
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
| | - Andrey E Boguslavskiy
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Ruaridh Forbes
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Iain Wilkinson
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Institute for Electronic Structure Dynamics, Helmholtz-Zentrum für Materialien und Energie, Hahn-Meitner-Platz 1, 14109 Berlin, Germany
| | - Rune Lausten
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Albert Stolow
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- NRC-uOttawa Joint Centre for Extreme and Quantum Photonics (JCEP), Ottawa, Ontario K1A 0R6, Canada
| | - Michael S Schuurman
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Paul Hockett
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Varun Makhija
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
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3
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Sahu A, Pg S, Madhok V. Effect of chaos on information gain in quantum tomography. Phys Rev E 2022; 106:024209. [PMID: 36109924 DOI: 10.1103/physreve.106.024209] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 07/29/2022] [Indexed: 06/15/2023]
Abstract
Does chaos in the dynamics enable or impede information gain in quantum tomography? We address this question by considering continuous measurement tomography in which the measurement record is obtained as a sequence of expectation values of a Hermitian observable evolving under the repeated application of the Floquet map of the quantum kicked top. For a given dynamics and Hermitian observables, we observe completely opposite behavior in the tomography of well-localized spin coherent states compared to random states. As the chaos in the dynamics increases, the reconstruction fidelity of spin coherent states decreases. This contrasts with the previous results connecting information gain in tomography of random states with the degree of chaos in the dynamics that drives the system. The rate of information gain and hence the fidelity obtained in tomography depends not only on the degree of chaos in the dynamics and to what extent it causes the initial observable to spread in various directions of the operator space, but, more importantly, how well these directions are aligned with the density matrix to be estimated. Our study also gives an operational interpretation for operator spreading in terms of fidelity gain in an actual quantum information tomography protocol.
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Affiliation(s)
- Abinash Sahu
- Mphasis Centre for Quantum Information, Communication and Computing (MCQuICC), Indian Institute of Technology Madras, Chennai 600036, India and Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Sreeram Pg
- Mphasis Centre for Quantum Information, Communication and Computing (MCQuICC), Indian Institute of Technology Madras, Chennai 600036, India and Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Vaibhav Madhok
- Mphasis Centre for Quantum Information, Communication and Computing (MCQuICC), Indian Institute of Technology Madras, Chennai 600036, India and Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
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4
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Evrard B, Qu A, Dalibard J, Gerbier F. Observation of fragmentation of a spinor Bose-Einstein condensate. Science 2021; 373:1340-1343. [PMID: 34529460 DOI: 10.1126/science.abd8206] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- Bertrand Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 75005 Paris, France
| | - An Qu
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 75005 Paris, France
| | - Fabrice Gerbier
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 75005 Paris, France
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5
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Hardy L, Lewis AGM. Quantum computation with machine-learning-controlled quantum stuff. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/abb215] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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7
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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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8
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Rocchetto A, Aaronson S, Severini S, Carvacho G, Poderini D, Agresti I, Bentivegna M, Sciarrino F. Experimental learning of quantum states. SCIENCE ADVANCES 2019; 5:eaau1946. [PMID: 30944851 PMCID: PMC6440753 DOI: 10.1126/sciadv.aau1946] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2018] [Accepted: 02/06/2019] [Indexed: 06/01/2023]
Abstract
The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.
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Affiliation(s)
- Andrea Rocchetto
- Department of Computer Science, University of Oxford, Oxford, UK
- Department of Computer Science, University College London, London, UK
| | - Scott Aaronson
- Department of Computer Science, University of Texas at Austin, Austin, USA
| | - Simone Severini
- Department of Computer Science, University College London, London, UK
- Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China
| | | | - Davide Poderini
- Dipartimento di Fisica–Sapienza Università di Roma, Rome, Italy
| | - Iris Agresti
- Dipartimento di Fisica–Sapienza Università di Roma, Rome, Italy
| | | | - Fabio Sciarrino
- Dipartimento di Fisica–Sapienza Università di Roma, Rome, Italy
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9
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Zhang L, Yu Y, Zhu C, Pei C. Noise tailoring for quantum circuits via unitary 2t-design. Sci Rep 2019; 9:1790. [PMID: 30741965 PMCID: PMC6370869 DOI: 10.1038/s41598-018-38158-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Accepted: 12/20/2018] [Indexed: 11/09/2022] Open
Abstract
Because of environmental variations and imperfect operations, real-world quantum computers produce different coherent errors that are difficult to estimate. Here, we propose a method whereby the twirled noise over a unitary 2t-design (a set of unitary matrices that approximate the entire unitary group) for quantum circuits can be tailored into stochastic noise. Then, we prove that local random circuits for twirling separable noisy channel over the Clifford group can be used to construct a unitary 2t-design, which is easy to implement in experiments. Moreover, we prove that our method is robust to gate-dependent and gate-independent noise. The stochastic noise can be both estimated by average fidelity and directly obtained by randomized benchmarking via unitary 2t-designs. Obtaining such tailored noise is an important guarantee for achieving fault-tolerant quantum computation.
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Affiliation(s)
- Linxi Zhang
- State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, 710071, China
- Science and Technology on Communication Networks Laboratory, Shijiazhuang, 050081, China
| | - Yan Yu
- State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, 710071, China.
| | - Changhua Zhu
- State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, 710071, China
| | - Changxing Pei
- State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, 710071, China
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10
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Banchi L, Kolthammer WS, Kim MS. Multiphoton Tomography with Linear Optics and Photon Counting. PHYSICAL REVIEW LETTERS 2018; 121:250402. [PMID: 30608836 DOI: 10.1103/physrevlett.121.250402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Indexed: 06/09/2023]
Abstract
Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary multimode state containing a definite number of photons, or an arbitrary mixture of such states. We show this task can be achieved using only linear optics and photon counting, which yield a practical though nonuniversal set of projective measurements. We derive the minimum number of measurement settings required and numerically show that this lower bound is saturated with random linear optics configurations, such as when the corresponding unitary transformation is Haar random. Furthermore, we show that for N photons, any unitary 2N design can be used to derive an analytical, though nonoptimal, state reconstruction protocol.
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Affiliation(s)
- Leonardo Banchi
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - W Steven Kolthammer
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - M S Kim
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
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11
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12
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Faist P, Renner R. Practical and Reliable Error Bars in Quantum Tomography. PHYSICAL REVIEW LETTERS 2016; 117:010404. [PMID: 27419548 DOI: 10.1103/physrevlett.117.010404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Indexed: 06/06/2023]
Abstract
Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis. Promising recent methods based on confidence regions are difficult to apply in practice or yield error bars which are unnecessarily large. Here, we propose a practical yet robust method for obtaining error bars. We do so by introducing a novel representation of the output of the tomography procedure, the quantum error bars. This representation is (i) concise, being given in terms of few parameters, (ii) intuitive, providing a fair idea of the "spread" of the error, and (iii) useful, containing the necessary information for constructing confidence regions. The statements resulting from our method are formulated in terms of a figure of merit, such as the fidelity to a reference state. We present an algorithm for computing this representation and provide ready-to-use software. Our procedure is applied to actual experimental data obtained from two superconducting qubits in an entangled state, demonstrating the applicability of our method.
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Affiliation(s)
- Philippe Faist
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Renato Renner
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
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13
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Heeg KP, Ott C, Schumacher D, Wille HC, Röhlsberger R, Pfeifer T, Evers J. Interferometric phase detection at x-ray energies via Fano resonance control. PHYSICAL REVIEW LETTERS 2015; 114:207401. [PMID: 26047250 DOI: 10.1103/physrevlett.114.207401] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2014] [Indexed: 06/04/2023]
Abstract
Modern x-ray light sources promise access to structure and dynamics of matter in largely unexplored spectral regions. However, the desired information is encoded in the light intensity and phase, whereas detectors register only the intensity. This phase problem is ubiquitous in crystallography and imaging and impedes the exploration of quantum effects at x-ray energies. Here, we demonstrate phase-sensitive measurements characterizing the quantum state of a nuclear two-level system at hard x-ray energies. The nuclei are initially prepared in a superposition state. Subsequently, the relative phase of this superposition is interferometrically reconstructed from the emitted x rays. Our results form a first step towards x-ray quantum state tomography and provide new avenues for structure determination and precision metrology via x-ray Fano interference.
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Affiliation(s)
- K P Heeg
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
| | - C Ott
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
| | - D Schumacher
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - H-C Wille
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - R Röhlsberger
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - T Pfeifer
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
| | - J Evers
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
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14
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Galetti E, Curtis A, Meles GA, Baptie B. Uncertainty loops in travel-time tomography from nonlinear wave physics. PHYSICAL REVIEW LETTERS 2015; 114:148501. [PMID: 25910166 DOI: 10.1103/physrevlett.114.148501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2014] [Indexed: 06/04/2023]
Abstract
Estimating image uncertainty is fundamental to guiding the interpretation of geoscientific tomographic maps. We reveal novel uncertainty topologies (loops) which indicate that while the speeds of both low- and high-velocity anomalies may be well constrained, their locations tend to remain uncertain. The effect is widespread: loops dominate around a third of United Kingdom Love wave tomographic uncertainties, changing the nature of interpretation of the observed anomalies. Loops exist due to 2nd and higher order aspects of wave physics; hence, although such structures must exist in many tomographic studies in the physical sciences and medicine, they are unobservable using standard linearized methods. Higher order methods might fruitfully be adopted.
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Affiliation(s)
- Erica Galetti
- School of GeoSciences, The University of Edinburgh, Grant Institute, The King's Buildings, James Hutton Road, Edinburgh EH9 3FE, United Kingdom
| | - Andrew Curtis
- School of GeoSciences, The University of Edinburgh, Grant Institute, The King's Buildings, James Hutton Road, Edinburgh EH9 3FE, United Kingdom
| | - Giovanni Angelo Meles
- School of GeoSciences, The University of Edinburgh, Grant Institute, The King's Buildings, James Hutton Road, Edinburgh EH9 3FE, United Kingdom
| | - Brian Baptie
- British Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 3LA, United Kingdom
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15
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Tonolini F, Chan S, Agnew M, Lindsay A, Leach J. Reconstructing high-dimensional two-photon entangled states via compressive sensing. Sci Rep 2014; 4:6542. [PMID: 25306850 PMCID: PMC4194436 DOI: 10.1038/srep06542] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Accepted: 09/12/2014] [Indexed: 12/04/2022] Open
Abstract
Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction procedures can become prohibitively time-consuming. Compressive sensing, a procedure for solving inverse problems by incorporating prior knowledge about the form of the solution, provides an attractive alternative to the problem of high-dimensional quantum state characterisation. Using a modified version of compressive sensing that incorporates the principles of singular value thresholding, we reconstruct the density matrix of a high-dimensional two-photon entangled system. The dimension of each photon is equal to d = 17, corresponding to a system of 83521 unknown real parameters. Accurate reconstruction is achieved with approximately 2500 measurements, only 3% of the total number of unknown parameters in the state. The algorithm we develop is fast, computationally inexpensive, and applicable to a wide range of quantum states, thus demonstrating compressive sensing as an effective technique for measuring the state of large-scale quantum systems.
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Affiliation(s)
- Francesco Tonolini
- SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Susan Chan
- SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Megan Agnew
- SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Alan Lindsay
- SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
- Applied and Computational Mathematics and Statistics, University of Notre Dame, USA
| | - Jonathan Leach
- SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
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16
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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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17
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Amico L, Rossini D, Hamma A, Korepin VE. Optimal correlations in many-body quantum systems. PHYSICAL REVIEW LETTERS 2012; 108:240503. [PMID: 23004247 DOI: 10.1103/physrevlett.108.240503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2011] [Revised: 04/20/2012] [Indexed: 06/01/2023]
Abstract
Information and correlations in a quantum system are closely related through the process of measurement. We explore such relation in a many-body quantum setting, effectively bridging between quantum metrology and condensed matter physics. To this aim we adopt the information-theory view of correlations and study the amount of correlations after certain classes of positive-operator-valued measurements are locally performed. As many-body systems, we consider a one-dimensional array of interacting two-level systems (a spin chain) at zero temperature, where quantum effects are most pronounced. We demonstrate how the optimal strategy to extract the correlations depends on the quantum phase through a subtle interplay between local interactions and coherence.
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Affiliation(s)
- L Amico
- CNR-MATIS-IMM and Dipartimento di Fisica e Astronomia, Università di Catania, C/O ed. 10, viale A. Doria 6, I-95125 Catania, Italy
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Dai HN, Zhang H, Yang SJ, Zhao TM, Rui J, Deng YJ, Li L, Liu NL, Chen S, Bao XH, Jin XM, Zhao B, Pan JW. Holographic storage of biphoton entanglement. PHYSICAL REVIEW LETTERS 2012; 108:210501. [PMID: 23003228 DOI: 10.1103/physrevlett.108.210501] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2012] [Revised: 03/20/2012] [Indexed: 06/01/2023]
Abstract
Coherent and reversible storage of multiphoton entanglement with a multimode quantum memory is essential for scalable all-optical quantum information processing. Although a single photon has been successfully stored in different quantum systems, storage of multiphoton entanglement remains challenging because of the critical requirement for coherent control of the photonic entanglement source, multimode quantum memory, and quantum interface between them. Here we demonstrate a coherent and reversible storage of biphoton Bell-type entanglement with a holographic multimode atomic-ensemble-based quantum memory. The retrieved biphoton entanglement violates the Bell inequality for 1 μs storage time and a memory-process fidelity of 98% is demonstrated by quantum state tomography.
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Affiliation(s)
- Han-Ning Dai
- 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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19
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Ishizaki A, Calhoun TR, Schlau-Cohen GS, Fleming GR. Quantum coherence and its interplay with protein environments in photosynthetic electronic energy transfer. Phys Chem Chem Phys 2010; 12:7319-37. [DOI: 10.1039/c003389h] [Citation(s) in RCA: 282] [Impact Index Per Article: 20.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
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20
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D'Auria V, Fornaro S, Porzio A, Solimeno S, Olivares S, Paris MGA. Full characterization of Gaussian bipartite entangled states by a single homodyne detector. PHYSICAL REVIEW LETTERS 2009; 102:020502. [PMID: 19257255 DOI: 10.1103/physrevlett.102.020502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2008] [Indexed: 05/27/2023]
Abstract
We present the full experimental reconstruction of Gaussian entangled states generated by a type-II optical parametric oscillator below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement, and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of optical parametric oscillator signals and represent a tool for quantum technology based on continuous variable entanglement.
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Affiliation(s)
- V D'Auria
- Dipartimento di Scienze Fisiche Università Federico II, Napoli, Italy
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21
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22
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D'Ariano GM, Perinotti P. Optimal data processing for quantum measurements. PHYSICAL REVIEW LETTERS 2007; 98:020403. [PMID: 17358587 DOI: 10.1103/physrevlett.98.020403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2006] [Indexed: 05/14/2023]
Abstract
We consider the general measurement scenario in which the ensemble average of an operator is determined via suitable data processing of the outcomes of a quantum measurement described by a positive operator-valued measure. We determine the optimal processing that minimizes the statistical error of the estimation.
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Affiliation(s)
- G M D'Ariano
- QUIT Group, Dipartimento di Fisica, Pavia, Italy
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23
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Katz N, Ansmann M, Bialczak RC, Lucero E, McDermott R, Neeley M, Steffen M, Weig EM, Cleland AN, Martinis JM, Korotkov AN. Coherent State Evolution in a Superconducting Qubit from Partial-Collapse Measurement. Science 2006; 312:1498-500. [PMID: 16763142 DOI: 10.1126/science.1126475] [Citation(s) in RCA: 141] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Measurement is one of the fundamental building blocks of quantum-information processing systems. Partial measurement, where full wavefunction collapse is not the only outcome, provides a detailed test of the measurement process. We introduce quantum-state tomography in a superconducting qubit that exhibits high-fidelity single-shot measurement. For the two probabilistic outcomes of partial measurement, we find either a full collapse or a coherent yet nonunitary evolution of the state. This latter behavior explicitly confirms modern quantum-measurement theory and may prove important for error-correction algorithms in quantum computation.
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Affiliation(s)
- N Katz
- Department of Physics and California NanoSystems Institute, University of California, Santa Barbara, CA 93106, USA
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25
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D Ariano GM, Perinotti P, Sacchi MF. Informationally complete measurements and group representation. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/1464-4266/6/6/005] [Citation(s) in RCA: 73] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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