Analysing quantum systems with randomised measurements

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 estim...

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Published inPhysics reports Vol. 1095; pp. 1 - 48
Main Authors Cieśliński, Paweł, Imai, Satoya, Dziewior, Jan, Gühne, Otfried, Knips, Lukas, Laskowski, Wiesław, Meinecke, Jasmin, Paterek, Tomasz, Vértesi, Tamás
Format Journal Article
LanguageEnglish
Published Elsevier B.V 05.12.2024
Subjects
Multipartite entanglement
Non-local correlations
Quantum designs
Randomised measurements
Quantum designs
Non-local correlations
Randomised measurements
Multipartite entanglement
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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. [Display omitted]
AbstractList 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. [Display omitted]
Author Laskowski, Wiesław
Meinecke, Jasmin
Vértesi, Tamás
Imai, Satoya
Gühne, Otfried
Dziewior, Jan
Paterek, Tomasz
Knips, Lukas
Cieśliński, Paweł
Author_xml – sequence: 1
  givenname: Paweł
  surname: Cieśliński
  fullname: Cieśliński, Paweł
  organization: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Gdańsk, 80-308, Poland
– sequence: 2
  givenname: Satoya
  surname: Imai
  fullname: Imai, Satoya
  organization: Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, Siegen, 57068, Germany
– sequence: 3
  givenname: Jan
  surname: Dziewior
  fullname: Dziewior, Jan
  organization: Max Planck Institute for Quantum Optics, Garching, 85748, Germany
– sequence: 4
  givenname: Otfried
  surname: Gühne
  fullname: Gühne, Otfried
  organization: Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, Siegen, 57068, Germany
– sequence: 5
  givenname: Lukas
  surname: Knips
  fullname: Knips, Lukas
  organization: Max Planck Institute for Quantum Optics, Garching, 85748, Germany
– sequence: 6
  givenname: Wiesław
  orcidid: 0000-0001-5166-0373
  surname: Laskowski
  fullname: Laskowski, Wiesław
  email: wieslaw.laskowski@ug.edu.pl
  organization: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Gdańsk, 80-308, Poland
– sequence: 7
  givenname: Jasmin
  surname: Meinecke
  fullname: Meinecke, Jasmin
  organization: Max Planck Institute for Quantum Optics, Garching, 85748, Germany
– sequence: 8
  givenname: Tomasz
  surname: Paterek
  fullname: Paterek, Tomasz
  organization: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Gdańsk, 80-308, Poland
– sequence: 9
  givenname: Tamás
  surname: Vértesi
  fullname: Vértesi, Tamás
  organization: MTA ATOMKI Lendület Quantum Correlations Research Group, Institute for Nuclear Research, Debrecen, 4001, Hungary
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Non-local correlations
Randomised measurements
Multipartite entanglement
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Snippet Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration....
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SubjectTerms Multipartite entanglement
Non-local correlations
Quantum designs
Randomised measurements
Title Analysing quantum systems with randomised measurements
URI https://dx.doi.org/10.1016/j.physrep.2024.09.009
Volume 1095
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