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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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Yang Y, Yadin B, Xu ZP. Quantum-Enhanced Metrology with Network States. PHYSICAL REVIEW LETTERS 2024; 132:210801. [PMID: 38856242 DOI: 10.1103/physrevlett.132.210801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 12/12/2023] [Accepted: 04/15/2024] [Indexed: 06/11/2024]
Abstract
Armed with quantum correlations, quantum sensors in a network have shown the potential to outclass their classical counterparts in distributed sensing tasks such as clock synchronization and reference frame alignment. On the other hand, this analysis was done for simple and idealized networks, whereas the correlation shared within a practical quantum network, captured by the notion of network states, is much more complex. Here, we prove a general bound that limits the performance of using quantum network states to estimate a global parameter, establishing the necessity of genuine multipartite entanglement for achieving a quantum advantage. The bound can also serve as an entanglement witness in networks and can be generalized to states generated by shallow circuits. Moreover, while our bound prohibits local network states from achieving the Heisenberg limit, we design a probabilistic protocol that, once successful, attains this ultimate limit of quantum metrology and preserves the privacy of involved parties. Our work establishes both the limitation and the possibility of quantum metrology within quantum networks.
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Affiliation(s)
- Yuxiang Yang
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Benjamin Yadin
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Zhen-Peng Xu
- School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, People's Republic of China
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3
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Luo MX. Quantumness speeds up quantum thermodynamics processes. iScience 2024; 27:109722. [PMID: 38689639 PMCID: PMC11059519 DOI: 10.1016/j.isci.2024.109722] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Revised: 03/26/2024] [Accepted: 04/08/2024] [Indexed: 05/02/2024] Open
Abstract
Quantum thermodynamic process involves manipulating and controlling quantum states to extract energy or perform computational tasks with high efficiency. There is still no efficient general method to theoretically quantify the effect of the quantumness of coherence and entanglement in work extraction. In this work, we propose a thermodynamics speed to quantify the extracting work. We show that the coherence of quantum systems can speed up work extracting with respect to some cyclic evolution beyond all incoherent states. We further show the genuine entanglement of quantum systems may speed up work extracting beyond any bi-separable states. This provides a new thermodynamic method to witness entangled systems with physical quantities.
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Affiliation(s)
- Ming-Xing Luo
- School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
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4
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Liu LZ, Fei YY, Mao Y, Hu Y, Zhang R, Yin XF, Jiang X, Li L, Liu NL, Xu F, Chen YA, Pan JW. Full-Period Quantum Phase Estimation. PHYSICAL REVIEW LETTERS 2023; 130:120802. [PMID: 37027851 DOI: 10.1103/physrevlett.130.120802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Accepted: 02/28/2023] [Indexed: 06/19/2023]
Abstract
Quantum sensing can provide the superior sensitivity for sensing a physical quantity beyond the shot-noise limit. In practice, however, this technique has been limited to the issues of phase ambiguity and low sensitivity for small-scale probe states. Here, we propose and demonstrate a full-period quantum phase estimation approach by adopting the Kitaev's phase estimation algorithm to eliminate the phase ambiguity and using the GHZ states to obtain phase value, simultaneously. For an N-party entangled state, our approach can achieve an upper bound of sensitivity of δθ=sqrt[3/(N^{2}+2N)], which beats the limit of adaptive Bayesian estimation. By performing an eight-photon experiment, we demonstrate the estimation of unknown phases in a full period, and observe the phase superresolution and sensitivity beyond the shot-noise limit. Our Letter provides a new way for quantum sensing and represents a solid step towards its general applications.
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Affiliation(s)
- Li-Zheng Liu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Yue-Yang Fei
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Yingqiu Mao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Yi Hu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Rui Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Xu-Fei Yin
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Xiao Jiang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Li Li
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Nai-Le Liu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Feihu Xu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yu-Ao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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5
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Ren Z, Li W, Smerzi A, Gessner M. Metrological Detection of Multipartite Entanglement from Young Diagrams. PHYSICAL REVIEW LETTERS 2021; 126:080502. [PMID: 33709723 DOI: 10.1103/physrevlett.126.080502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
We characterize metrologically useful multipartite entanglement by representing partitions with Young diagrams. We derive entanglement witnesses that are sensitive to the shape of Young diagrams and show that Dyson's rank acts as a resource for quantum metrology. Common quantifiers, such as the entanglement depth and k-separability are contained in this approach as the diagram's width and height. Our methods are experimentally accessible in a wide range of atomic systems, as we illustrate by analyzing published data on the quantum Fisher information and spin-squeezing coefficients.
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Affiliation(s)
- Zhihong Ren
- Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
| | - Weidong Li
- Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Augusto Smerzi
- Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Manuel Gessner
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
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6
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Quantifying computational advantage of Grover's algorithm with the trace speed. Sci Rep 2021; 11:1288. [PMID: 33446696 PMCID: PMC7809032 DOI: 10.1038/s41598-020-80153-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Accepted: 11/09/2020] [Indexed: 11/08/2022] Open
Abstract
Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we report a close connection between the trace speed and the quantum speed-up in Grover's search algorithm implemented with pure and pseudo-pure states. For a noiseless algorithm, we find a one-to-one correspondence between the quantum speed-up and the polarization of the pseudo-pure state, which can be connected to a wide class of quantum statistical speeds. For time-dependent partial depolarization and for interrupted Grover searches, the speed-up is specifically bounded by the maximal trace speed that occurs during the algorithm operations. Our results quantify the quantum speed-up with a physical resource that is experimentally measurable and related to multipartite entanglement and quantum coherence.
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7
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8
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Gabbrielli M, Smerzi A, Pezzè L. Multipartite Entanglement at Finite Temperature. Sci Rep 2018; 8:15663. [PMID: 30353077 PMCID: PMC6199326 DOI: 10.1038/s41598-018-31761-3] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2018] [Accepted: 08/17/2018] [Indexed: 11/10/2022] Open
Abstract
The interplay of quantum and thermal fluctuations in the vicinity of a quantum critical point characterizes the physics of strongly correlated systems. Here we investigate this interplay from a quantum information perspective presenting the universal phase diagram of the quantum Fisher information at a quantum phase transition. Different regions in the diagram are identified by characteristic scaling laws of the quantum Fisher information with respect to temperature. This feature has immediate consequences on the thermal robustness of quantum coherence and multipartite entanglement. We support the theoretical predictions with the analysis of paradigmatic spin systems showing symmetry-breaking quantum phase transitions and free-fermion models characterized by topological phases. In particular we show that topological systems are characterized by the survival of large multipartite entanglement, reaching the Heisenberg limit at finite temperature.
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Affiliation(s)
- Marco Gabbrielli
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy
| | - Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy.
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9
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Zhang YR, Zeng Y, Fan H, You JQ, Nori F. Characterization of Topological States via Dual Multipartite Entanglement. PHYSICAL REVIEW LETTERS 2018; 120:250501. [PMID: 29979055 DOI: 10.1103/physrevlett.120.250501] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2017] [Revised: 03/29/2018] [Indexed: 06/08/2023]
Abstract
We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the spin operators defined in the dual lattice. We investigate an extended Kitaev chain with a Z symmetry identified equivalently by winding numbers and paired Majorana zero modes at each end. The topological phases with high winding numbers are detected by the scaling coefficient of the quantum Fisher information density with respect to generators in different dual lattices. Containing richer properties and more complex structures than bipartite entanglement, the dual multipartite entanglement of the topological state has promising applications in robust quantum computation and quantum metrology, and can be generalized to identify topological order in the Kitaev honeycomb model.
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Affiliation(s)
- Yu-Ran Zhang
- Beijing Computational Science Research Center, Beijing 100193, China
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Yu Zeng
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, UCAS, Beijing 100190, China
| | - J Q You
- Beijing Computational Science Research Center, Beijing 100193, China
- Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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10
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Pezzè L, Gabbrielli M, Lepori L, Smerzi A. Multipartite Entanglement in Topological Quantum Phases. PHYSICAL REVIEW LETTERS 2017; 119:250401. [PMID: 29303346 DOI: 10.1103/physrevlett.119.250401] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2017] [Indexed: 06/07/2023]
Abstract
We witness multipartite entanglement in the ground state of the Kitaev chain-a benchmark model of a one dimensional topological superconductor-also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, for both short- and long-range pairing, are characterized by a power-law diverging finite-size scaling of multipartite entanglement. Moreover, the occurring quantum phase transitions are sharply marked by the divergence of the derivative of the quantum Fisher information, even in the absence of a closing energy gap.
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Affiliation(s)
- Luca Pezzè
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Marco Gabbrielli
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Luca Lepori
- Dipartimento di Scienze Fisiche e Chimiche, Università dell'Aquila, via Vetoio 42, I-67010 Coppito-L'Aquila, Italy
- INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, I-67100 Assergi (AQ), Italy
| | - Augusto Smerzi
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
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11
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Pezzè L, Ciampini MA, Spagnolo N, Humphreys PC, Datta A, Walmsley IA, Barbieri M, Sciarrino F, Smerzi A. Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases. PHYSICAL REVIEW LETTERS 2017; 119:130504. [PMID: 29341700 DOI: 10.1103/physrevlett.119.130504] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Indexed: 06/07/2023]
Abstract
A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.
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Affiliation(s)
- Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Mario A Ciampini
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Nicolò Spagnolo
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Peter C Humphreys
- Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Ian A Walmsley
- Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Marco Barbieri
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
| | - Fabio Sciarrino
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
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