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Zhang C, Zhang WH, Sekatski P, Bancal JD, Zwerger M, Yin P, Li GC, Peng XX, Chen L, Han YJ, Xu JS, Huang YF, Chen G, Li CF, Guo GC. Certification of Genuine Multipartite Entanglement with General and Robust Device-Independent Witnesses. PHYSICAL REVIEW LETTERS 2022; 129:190503. [PMID: 36399745 DOI: 10.1103/physrevlett.129.190503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Accepted: 09/28/2022] [Indexed: 06/16/2023]
Abstract
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
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Affiliation(s)
- Chao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Wen-Hao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Pavel Sekatski
- Department of Applied Physics, University of Geneva, Rue de l'École-de-Médecine, 1211 Geneva, Switzerland
| | - Jean-Daniel Bancal
- Université Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191 Gif-sur-Yvette, France
| | - Michael Zwerger
- Max Planck Institute for the Science of Light, Erlangen 91058, Germany
| | - Peng Yin
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Gong-Chu Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Xing-Xiang Peng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Lei Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yong-Jian Han
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yun-Feng Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Geng Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, 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, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 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, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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Miguel-Ramiro J, Riera-Sàbat F, Dür W. Collective Operations Can Exponentially Enhance Quantum State Verification. PHYSICAL REVIEW LETTERS 2022; 129:190504. [PMID: 36399726 DOI: 10.1103/physrevlett.129.190504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Revised: 08/15/2022] [Accepted: 10/03/2022] [Indexed: 06/16/2023]
Abstract
Maximally entangled states are a key resource in many quantum communication and computation tasks, and their certification is a crucial element to guarantee the desired functionality. We introduce collective strategies for the efficient, local verification of ensembles of Bell pairs that make use of an initial information and noise transfer to few copies prior to their measurement. In this way the number of entangled pairs that need to be measured and hence destroyed is significantly reduced as compared to previous, even optimal, approaches that operate on individual copies. Moreover, the remaining states are directly certified. We show that our tools can be extended to other problems and larger classes of multipartite states.
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Affiliation(s)
- Jorge Miguel-Ramiro
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
| | - Ferran Riera-Sàbat
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
| | - Wolfgang Dür
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
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Zhang RQ, Hou Z, Tang JF, Shang J, Zhu H, Xiang GY, Li CF, Guo GC. Efficient Experimental Verification of Quantum Gates with Local Operations. PHYSICAL REVIEW LETTERS 2022; 128:020502. [PMID: 35089730 DOI: 10.1103/physrevlett.128.020502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Accepted: 11/24/2021] [Indexed: 06/14/2023]
Abstract
Verifying the correct functioning of quantum gates is a crucial step toward reliable quantum information processing, but it becomes an overwhelming challenge as the system size grows due to the dimensionality curse. Recent theoretical breakthroughs show that it is possible to verify various important quantum gates with the optimal sample complexity of O(1/ε) using local operations only, where ε is the estimation precision. In this Letter, we propose a variant of quantum gate verification (QGV) that is robust to practical gate imperfections and experimentally realize efficient QGV on a 2-qubit controlled-not gate and a 3-qubit Toffoli gate using only local state preparations and measurements. The experimental results show that, by using only 1600 and 2600 measurements on average, we can verify with 95% confidence level that the implemented controlled-not gate and Toffoli gate have fidelities of at least 99% and 97%, respectively. Demonstrating the superior low sample complexity and experimental feasibility of QGV, our work promises a solution to the dimensionality curse in verifying large quantum devices in the quantum era.
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Affiliation(s)
- Rui-Qi Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zhibo Hou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jun-Feng Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jiangwei Shang
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Huangjun Zhu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China
- Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China
| | - Guo-Yong Xiang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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Zhang X, Luo M, Wen Z, Feng Q, Pang S, Luo W, Zhou X. Direct Fidelity Estimation of Quantum States Using Machine Learning. PHYSICAL REVIEW LETTERS 2021; 127:130503. [PMID: 34623828 DOI: 10.1103/physrevlett.127.130503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Revised: 08/04/2021] [Accepted: 08/17/2021] [Indexed: 06/13/2023]
Abstract
In almost all quantum applications, one of the key steps is to verify that the fidelity of the prepared quantum state meets expectations. In this Letter, we propose a new approach solving this problem using machine-learning techniques. Compared to other fidelity estimation methods, our method is applicable to arbitrary quantum states, the number of required measurement settings is small, and this number does not increase with the size of the system. For example, for a general five-qubit quantum state, only four measurement settings are required to predict its fidelity with ±1% precision in a nonadversarial scenario. This machine-learning-based approach for estimating quantum state fidelity has the potential to be widely used in the field of quantum information.
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Affiliation(s)
- Xiaoqian Zhang
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
| | - Maolin Luo
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
| | - Zhaodi Wen
- College of Information Science and Technology, College of Cyber Security, Jinan University, Guangzhou 510632, China
| | - Qin Feng
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
| | - Shengshi Pang
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
| | - Weiqi Luo
- College of Information Science and Technology, College of Cyber Security, Jinan University, Guangzhou 510632, China
| | - Xiaoqi Zhou
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
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Liu YC, Shang J, Han R, Zhang X. Universally Optimal Verification of Entangled States with Nondemolition Measurements. PHYSICAL REVIEW LETTERS 2021; 126:090504. [PMID: 33750148 DOI: 10.1103/physrevlett.126.090504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 01/26/2021] [Indexed: 06/12/2023]
Abstract
The efficient and reliable characterization of quantum states plays a vital role in most, if not all, quantum information processing tasks. In this work, we present a universally optimal protocol for verifying entangled states by employing the so-called quantum nondemolition measurements, such that the verification efficiency is equivalent to that of the optimal global strategy. Instead of being probabilistic as the standard verification strategies, our protocol is constructed sequentially, which is thus more favorable for experimental realizations. In addition, the target states are preserved in the protocol after each measurement, so can be reused in any subsequent tasks. We demonstrate the power of our protocol for the optimal verification of Bell states, arbitrary two-qubit pure states, and stabilizer states. We also prove that our protocol is able to perform tasks including fidelity estimation and state preparation.
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Affiliation(s)
- Ye-Chao Liu
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Jiangwei Shang
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Rui Han
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
| | - Xiangdong Zhang
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
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7
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Elben A, Kueng R, Huang HYR, van Bijnen R, Kokail C, Dalmonte M, Calabrese P, Kraus B, Preskill J, Zoller P, Vermersch B. Mixed-State Entanglement from Local Randomized Measurements. PHYSICAL REVIEW LETTERS 2020; 125:200501. [PMID: 33258654 DOI: 10.1103/physrevlett.125.200501] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2020] [Accepted: 10/20/2020] [Indexed: 06/12/2023]
Abstract
We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by postprocessing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges et al., Science 364, 260 (2019)SCIEAS0036-807510.1126/science.aau4963].
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Affiliation(s)
- Andreas Elben
- Center for Quantum 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
| | - Richard Kueng
- Institute for Integrated Circuits, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria
| | - Hsin-Yuan Robert Huang
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
- Department of Computing and Mathematical Sciences, Caltech, Pasadena, California 91125, USA
| | - Rick van Bijnen
- Center for Quantum 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
| | - Christian Kokail
- Center for Quantum 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
| | - Marcello Dalmonte
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea 265, 34136 Trieste, Italy
| | - Pasquale Calabrese
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea 265, 34136 Trieste, Italy
- INFN, via Bonomea 265, 34136 Trieste, Italy
| | - Barbara Kraus
- Institute for Theoretical Physics, University of Innsbruck, A6020 Innsbruck, Austria
| | - John Preskill
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
- Department of Computing and Mathematical Sciences, Caltech, Pasadena, California 91125, USA
- Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, USA
- AWS Center for Quantum Computing, Pasadena, California 91125, USA
| | - Peter Zoller
- Center for Quantum 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
- Center for Quantum 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
- Université Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
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Zhou Y, Zeng P, Liu Z. Single-Copies Estimation of Entanglement Negativity. PHYSICAL REVIEW LETTERS 2020; 125:200502. [PMID: 33258639 DOI: 10.1103/physrevlett.125.200502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Accepted: 09/10/2020] [Indexed: 06/12/2023]
Abstract
Entanglement plays a central role in quantum information processing and quantum physics. However, few effective ways are known to detect the amount of entanglement of an unknown quantum state. Here, we propose a scheme to estimate the entanglement negativity for any bipartition of a composite system. The proposed scheme is based on the random unitary evolution and local measurements on a single-copy quantum state, which is more practical compared to former methods based on collective measurements on many copies of the identical state. Meanwhile, we generalize the scheme to quantify the total correlation. We demonstrate the efficiency of the scheme with statistical analyses and numerical simulations. Our scheme is quite suitable for state-of-the-art quantum platforms, which can serve as a useful benchmarking tool to advance quantum technologies and a probe to study fundamental quantum physics like entanglement dynamics.
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Affiliation(s)
- You Zhou
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Pei Zeng
- 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
- School of Physics, Peking University, Beijing 100871, China
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