Analysing quantum systems with randomised measurements
Year: 2024
Authors: Cieslinski P., Imai S., Dziewior J., G’uhne O., Knips L., Laskowski W., Meinecke J., Paterek T., Vyrtesi T.
Autors Affiliation: Univ Gdansk, Inst Theoret Phys & Astrophys, PL-80308 Gdansk, Poland; Univ Siegen, Naturwissensch Tech Fak, Walter Flex Str 3, D-57068 Siegen, Germany; CNR, INO, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Max Planck Inst Quantum Opt, D-85748 Garching, Germany; Ludwig Maximilians Univ Munchen, Fac Phys, D-80799 Munich, Germany; Munich Ctr Quantum Sci & Technol, D-80799 Munich, Germany; Univ Gdansk, Int Ctr Theory Quantum Technol, PL-80308 Gdansk, Poland; Tech Univ Berlin, Inst Festkorperphys, D-10623 Berlin, Germany; Xiamen Univ Malaysia, Sch Math & Phys, Sepang 43900, Malaysia; Inst Nucl Res, MTA ATOMK Lendulet Quantum Correlat Res Grp, H-4001 Debrecen, Hungary.
Abstract: Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum computing when dealing with noisy environments, and allow the estimation of properties of complex quantum systems in an easy and efficient manner. In this review, we present the advancements made in utilising randomised measurements in various scenarios of quantum information science. We describe how to detect and characterise different forms of entanglement, including genuine multipartite entanglement and bound entanglement. Bell inequalities are discussed to be typically violated even with randomised measurements, especially for a growing number of particles and settings. Furthermore, we also present an overview on the estimation of non-linear functions of quantum states and shadow tomography from randomised measurements. Throughout the review, we complement the description of theoretical ideas by explaining key experiments. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Journal/Review: PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
Volume: 1095 Pages from: 1 to: 48
More Information: We thank Jan L. Bonsel, Borivoje Dakic, Qiongyi He, Marcus Huber, Daniel E. Jones, Andreas Ketterer, Waldemar Klobus, Brian T. Kirby, Shuheng Liu, Zhenhuan Liu, Xiongfeng Ma, Simon Morelli, Stefan Nimmrichter, Aniket Rath, Peter J. Shadbolt, Shravan Shravan, Jens Siewert, Geza Toth, Minh Cong Tran, Michael Tschaffon, Julio I. de Vicente, Giuseppe Vitagliano, Harald Weinfurter, Nikolai Wyderka, Xiao-Dong Yu, and Yuan-Yuan Zhao, for discussions and collaborations on the subject. This work has been supported by the DAAD, Germany, the Deutsche Forschungsgemeinschaft, Germany (DFG, German Research Foundation, project numbers 447948357 and 440958198) , the DFG, Germany under Germany’s Excellence Strategy – EXC-2111 – 390814868 (Munich Center for Quantum Science and Technology) , the Sino-German Center for Research Promotion, Germany (Project M-0294) , the ERC (Consolidator Grant 683107/TempoQ) , the German Ministry of Education and Research (Project QuKuK, BMBF Grant No. 16KIS1618K and 16KIS1621) , the National Science Centre (NCN, Poland) within the Preludium Bis project (Grant No. 2021/43/O/ST2/02679) , the Xiamen University Malaysia Research Fund (Grant No. XMUMRF/2022-C10/IPHY/0002) , the EU (QuantERA eDICT, CHIST-ERA MoDIC) , and the National Research, Development and Innovation Office NKFIH, Hungary (No. 2019-2.1.7-ERA-NET-2020-00003, 2023-1.2.1-ERA_NET-2023-00009, and K145927) .KeyWords: Randomised measurements; Quantum designs; Multipartite entanglement; Non-local correlationsDOI: 10.1016/j.physrep.2024.09.009
