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Yadin B, Imai S, Gühne O. Quantum Speed Limit for States and Observables of Perturbed Open Systems. PHYSICAL REVIEW LETTERS 2024; 132:230404. [PMID: 38905682 DOI: 10.1103/physrevlett.132.230404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Revised: 03/01/2024] [Accepted: 05/06/2024] [Indexed: 06/23/2024]
Abstract
Quantum speed limits provide upper bounds on the rate with which a quantum system can move away from its initial state. Here, we provide a different kind of speed limit, describing the divergence of a perturbed open system from its unperturbed trajectory. In the case of weak coupling, we show that the divergence speed is bounded by the quantum Fisher information under a perturbing Hamiltonian, up to an error which can be estimated from system and bath timescales. We give three applications of our speed limit. First, it enables experimental estimation of quantum Fisher information in the presence of decoherence that is not fully characterized. Second, it implies that large quantum work fluctuations are necessary for a thermal system to be driven quickly out of equilibrium under a quench. Moreover, it can be used to bound the response to perturbations of expectation values of observables in open systems.
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2
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Naldesi P, Elben A, Minguzzi A, Clément D, Zoller P, Vermersch B. Fermionic Correlation Functions from Randomized Measurements in Programmable Atomic Quantum Devices. PHYSICAL REVIEW LETTERS 2023; 131:060601. [PMID: 37625073 DOI: 10.1103/physrevlett.131.060601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 03/16/2023] [Indexed: 08/27/2023]
Abstract
We provide an efficient randomized measurement protocol to estimate two- and four-point fermionic correlations in ultracold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical landscapes, with high-resolution imaging systems such as quantum gas microscopes. We illustrate our results in the context of the variational quantum eigensolver algorithm for solving quantum chemistry problems.
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Affiliation(s)
- Piero Naldesi
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Andreas Elben
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
- Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, USA
| | - Anna Minguzzi
- Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
| | - David Clément
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127, Palaiseau, France
| | - Peter Zoller
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Benoît Vermersch
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
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3
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Shen Y, Soh HY, Kwek LC, Fan W. Fisher Information as General Metrics of Quantum Synchronization. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1116. [PMID: 37628145 PMCID: PMC10453851 DOI: 10.3390/e25081116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Revised: 07/14/2023] [Accepted: 07/24/2023] [Indexed: 08/27/2023]
Abstract
Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is currently no widely agreed metric that is universally adopted. In this paper, we propose using classical and quantum Fisher information (FI) as alternative metrics to detect and measure quantum synchronization. We establish the connection between FI and quantum synchronization, demonstrating that both classical and quantum FI can be deployed as more general indicators of quantum phase synchronization in some regimes where all other existing measures fail to provide reliable results. We show advantages in FI-based measures, especially in 2-to-1 synchronization. Furthermore, we analyze the impact of noise on the synchronization measures, revealing the robustness and susceptibility of each method in the presence of dissipation and decoherence. Our results open up new avenues for understanding and exploiting quantum synchronization.
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Affiliation(s)
- Yuan Shen
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, Singapore 639798, Singapore
| | - Hong Yi Soh
- National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
| | - Leong-Chuan Kwek
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, Singapore 639798, Singapore
- National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore 117543, Singapore
| | - Weijun Fan
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, Singapore 639798, Singapore
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Šafránek D, Rosa D, Binder FC. Work Extraction from Unknown Quantum Sources. PHYSICAL REVIEW LETTERS 2023; 130:210401. [PMID: 37295083 DOI: 10.1103/physrevlett.130.210401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 04/07/2023] [Indexed: 06/12/2023]
Abstract
Energy extraction is a central task in thermodynamics. In quantum physics, ergotropy measures the amount of work extractable under cyclic Hamiltonian control. As its full extraction requires perfect knowledge of the initial state, however, it does not characterize the work value of unknown or untrusted quantum sources. Fully characterizing such sources would require quantum tomography, which is prohibitively costly in experiments due to the exponential growth of required measurements and operational limitations. Here, we therefore derive a new notion of ergotropy applicable when nothing is known about the quantum states produced by the source, apart from what can be learned by performing only a single type of coarse-grained measurement. We find that in this case the extracted work is defined by the Boltzmann and observational entropy in cases where the measurement outcomes are, or are not, used in the work extraction, respectively. This notion of ergotropy represents a realistic measure of extractable work, which can be used as the relevant figure of merit to characterize a quantum battery.
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Affiliation(s)
- Dominik Šafránek
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon - 34126, Korea
| | - Dario Rosa
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon - 34126, Korea
- Basic Science Program, Korea University of Science and Technology (UST), Daejeon-34113, Korea
| | - Felix C Binder
- School of Physics, Trinity College Dublin, Dublin 2, Ireland
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McNulty D, Maciejewski FB, Oszmaniec M. Estimating Quantum Hamiltonians via Joint Measurements of Noisy Noncommuting Observables. PHYSICAL REVIEW LETTERS 2023; 130:100801. [PMID: 36962023 DOI: 10.1103/physrevlett.130.100801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 01/27/2023] [Indexed: 06/18/2023]
Abstract
Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this Letter, we introduce a method for this purpose based on performing a single joint measurement that can be implemented locally and whose marginals yield noisy (unsharp) versions of the target set of noncommuting Pauli observables. We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision. We compare this strategy to the classical shadow formalism and show that our method yields the same performance as the locally biased classical shadow protocol. We also highlight some general connections between the two approaches by showing that classical shadows can be used to construct joint measurements and vice versa. Finally, we adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy. This can provide significant efficiency improvements compared to known generalizations of classical shadows to noisy scenarios.
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Affiliation(s)
- Daniel McNulty
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
| | - Filip B Maciejewski
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
| | - Michał Oszmaniec
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
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Liu Z, Tang Y, Dai H, Liu P, Chen S, Ma X. Detecting Entanglement in Quantum Many-Body Systems via Permutation Moments. PHYSICAL REVIEW LETTERS 2022; 129:260501. [PMID: 36608179 DOI: 10.1103/physrevlett.129.260501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 11/15/2022] [Indexed: 06/17/2023]
Abstract
Multipartite entanglement plays an essential role in both quantum information science and many-body physics. Because of the exponentially large dimension and complex geometric structure of the state space, the detection of entanglement in many-body systems is extremely challenging in reality. Conventional means, like entanglement witness and entropy criterion, either highly depend on the prior knowledge of the studied systems or the detection capability is relatively weak. In this Letter, we propose a framework for designing multipartite entanglement criteria based on permutation moments, which have an effective implementation with either the generalized control-swap quantum circuits or the random unitary techniques. As an example, in the bipartite scenario, we develop an entanglement criterion that can detect bound entanglement and show strong detection capability in the multiqubit Ising model with a long-range XY Hamiltonian. In the multipartite case, the permutation-moment-based criteria can detect entangled states that are not detectable by any criteria extended from the bipartite case. Our framework also shows potential in entanglement quantification and entanglement structure detection.
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Affiliation(s)
- Zhenhuan Liu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Yifan Tang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
- Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
| | - Hao Dai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Pengyu Liu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Shu Chen
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Xiongfeng Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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Płodzień M, Lewenstein M, Witkowska E, Chwedeńczuk J. One-Axis Twisting as a Method of Generating Many-Body Bell Correlations. PHYSICAL REVIEW LETTERS 2022; 129:250402. [PMID: 36608238 DOI: 10.1103/physrevlett.129.250402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2022] [Accepted: 11/14/2022] [Indexed: 06/17/2023]
Abstract
We demonstrate that the one-axis twisting (OAT), a versatile method of creating nonclassical states of bosonic qubits, is a powerful source of many-body Bell correlations. We develop a fully analytical and universal treatment of the process, which allows us to identify the critical time at which the Bell correlations emerge and predict the depth of Bell correlations at all subsequent times. Our findings are illustrated with a highly nontrivial example of the OAT dynamics generated using the Bose-Hubbard model.
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Affiliation(s)
- Marcin Płodzień
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA, Passeig Lluís Companys 23, 08010 Barcelona, Spain
| | - Emilia Witkowska
- Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland
| | - Jan Chwedeńczuk
- Faculty of Physics, University of Warsaw, ulica Pasteura 5, PL-02-093 Warsaw, Poland
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Liu P, Liu Z, Chen S, Ma X. Fundamental Limitation on the Detectability of Entanglement. PHYSICAL REVIEW LETTERS 2022; 129:230503. [PMID: 36563217 DOI: 10.1103/physrevlett.129.230503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponentially many resources with regard to system size or qubit number, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic method to evaluate the detection capability of entanglement criteria theoretically. For a system coupled to an environment, we prove that any entanglement criterion needs exponentially many observables to detect the entanglement effectively when restricted to single-copy operations. Otherwise, the detection capability of the criterion will decay double exponentially. Furthermore, if multicopy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems. Our results may shed light on why quantum phenomena are difficult to observe in large noisy systems.
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Affiliation(s)
- Pengyu Liu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Zhenhuan Liu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Shu Chen
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Xiongfeng Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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Nguyen HC, Bönsel JL, Steinberg J, Gühne O. Optimizing Shadow Tomography with Generalized Measurements. PHYSICAL REVIEW LETTERS 2022; 129:220502. [PMID: 36493431 DOI: 10.1103/physrevlett.129.220502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 10/27/2022] [Accepted: 10/31/2022] [Indexed: 06/17/2023]
Abstract
Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system. Traditional tomography is limited to a handful of qubits, and shadow tomography has been suggested as a scalable replacement for larger systems. Shadow tomography is conventionally analyzed based on outcomes of ideal projective measurements on the system upon application of randomized unitaries. Here, we suggest that shadow tomography can be much more straightforwardly formulated for generalized measurements, or positive operator valued measures. Based on the idea of the least-square estimator shadow tomography with generalized measurements is both more general and simpler than the traditional formulation with randomization of unitaries. In particular, this formulation allows us to analyze theoretical aspects of shadow tomography in detail. For example, we provide a detailed study of the implication of symmetries in shadow tomography. Moreover, with this generalization we also demonstrate how the optimization of measurements for shadow tomography tailored toward a particular set of observables can be carried out.
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Affiliation(s)
- H Chau Nguyen
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Jan Lennart Bönsel
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Jonathan Steinberg
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
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Chang S, Ye W, Rao X, Zhang H, Huang L, Luo M, Chen Y, Gao S, Hu L. Evaluating the quantum Ziv-Zakai bound for phase estimation in noisy environments. OPTICS EXPRESS 2022; 30:24207-24221. [PMID: 36236980 DOI: 10.1364/oe.459659] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 06/08/2022] [Indexed: 06/16/2023]
Abstract
In the highly non-Gaussian regime, the quantum Ziv-Zakai bound (QZZB) provides a lower bound on the available precision, demonstrating the better performance compared with the quantum Cramér-Rao bound. However, evaluating the impact of a noisy environment on the QZZB without applying certain approximations proposed by Tsang [Phys. Rev. Lett.108, 230401 (2012)10.1103/PhysRevLett.108.230401] remains a difficult challenge. In this paper, we not only derive the asymptotically tight QZZB for phase estimation with the photon loss and the phase diffusion by invoking the variational method and the technique of integration within an ordered product of operators, but also show its estimation performance for several different Gaussian resources, such as a coherent state (CS), a single-mode squeezed vacuum state (SMSVS) and a two-mode squeezed vacuum state (TMSVS). In this asymptotically tight situation, our results indicate that compared with the SMSVS and the TMSVS, the QZZB for the CS always shows the better estimation performance under the photon-loss environment. More interestingly, for the phase-diffusion environment, the estimation performance of the QZZB for the TMSVS can be better than that for the CS throughout a wide range of phase-diffusion strength. Our findings will provide an useful guidance for investigating the noisy quantum parameter estimation.
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