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Xu L, Zhou M, Tao R, Zhong Z, Wang B, Cao Z, Xia H, Wang Q, Zhan H, Zhang A, Yu S, Xu N, Dong Y, Ren C, Zhang L. Resource-Efficient Direct Characterization of General Density Matrix. PHYSICAL REVIEW LETTERS 2024; 132:030201. [PMID: 38307054 DOI: 10.1103/physrevlett.132.030201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 11/27/2023] [Indexed: 02/04/2024]
Abstract
Sequential weak measurements allow for the direct extraction of individual density-matrix elements, rather than relying on global reconstruction of the entire density matrix, which opens a new avenue for the characterization of quantum systems. Nevertheless, extending the sequential scheme to multiqudit quantum systems is challenging due to the requirement of multiple coupling processes for each qudit and the lack of appropriate precision evaluation. To address these issues, we propose a resource-efficient scheme (RES) that directly characterizes the density matrix of general multiqudit systems while optimizing measurements and establishing a feasible estimation analysis. In the RES, an efficient observable of the quantum system is constructed such that a single meter state coupled to each qudit is sufficient to extract the corresponding density-matrix element. An appropriate model based on the statistical distribution of errors is utilized to evaluate the precision and feasibility of the scheme. We have experimentally applied the RES to the direct characterization of general single-photon qutrit states and two-photon entangled states. The results show that the RES outperforms sequential schemes in terms of efficiency and precision in both weak- and strong-coupling scenarios. This Letter sheds new light on the practical characterization of large-scale quantum systems and the investigation of their nonclassical properties.
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Affiliation(s)
- Liang Xu
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Mingti Zhou
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Runxia Tao
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Zhipeng Zhong
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Ben Wang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Zhiyong Cao
- School of Electronic Control, Chang'an University, Xi'an 710064, China
| | - Hongkuan Xia
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Qianyi Wang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Hao Zhan
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Aonan Zhang
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - Shang Yu
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - Nanyang Xu
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Ying Dong
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Changliang Ren
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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Li J, Luo Z, Xin T, Wang H, Kribs D, Lu D, Zeng B, Laflamme R. Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-Spin System. PHYSICAL REVIEW LETTERS 2019; 123:030502. [PMID: 31386459 DOI: 10.1103/physrevlett.123.030502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2018] [Indexed: 06/10/2023]
Abstract
Quantum pseudorandomness, also known as unitary designs, comprises a powerful resource for emergent quantum technologies. Although in theory pseudorandom unitary operators can be constructed efficiently, realizing these objects in realistic physical systems is a challenging task. Here, we demonstrate experimental generation and detection of quantum pseudorandomness on a 12-qubit nuclear magnetic resonance system. We first apply random sequences to the interacting nuclear spins, leading to random quantum evolutions that can quickly form unitary designs. Then, in order to probe the growth of quantum pseudorandomness during the time evolutions, we propose the idea of using the system's multiple-quantum coherence distribution as an indicator. Based on this indicator, we measure the spreading of quantum coherences and find that substantial quantum pseudorandomness has been achieved at the 12-qubit scale. This may open up a path to experimentally explore quantum randomness on forthcoming large-scale quantum processors.
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Affiliation(s)
- Jun Li
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518055, China
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Zhihuang Luo
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518055, China
- Laboratory of Quantum Engineering and Quantum Metrology, School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China
| | - Tao Xin
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Hengyan Wang
- Department of Physics, Zhejiang University of Science and Technology, Hangzhou 310023, China
| | - David Kribs
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Department of Mathematics & Statistics, University of Guelph, Guelph N1G 2W1, Ontario, Canada
| | - Dawei Lu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Bei Zeng
- Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518055, China
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Department of Mathematics & Statistics, University of Guelph, Guelph N1G 2W1, Ontario, Canada
| | - Raymond Laflamme
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Perimeter Institute for Theoretical Physics, Waterloo N2L 2Y5, Ontario, Canada
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