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Eigenvalue-based quantum state verification of three-qubit W class states

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  • Bao, Daipengwei
  • Liu, Min
  • Ou, Yangwei
  • Xu, Qingshan
  • Li, Qin
  • Tan, Xiaoqing

Abstract

In quantum many-body systems, W class states are typical examples of states with genuine multipartite entanglement. They have been found to be valuable resources in many quantum information processing tasks. However, the characterization and verification of W class states still remains an intractable problem. Here we first propose an eigenvalue-based verification protocol consisting of four practical adaptive local projective measurement tests, and obtain the optimal test probabilities with particle swarm optimization algorithm. The efficiency achieved by this protocol is far from satisfactory when compared with the theoretical upper bound. Then by utilizing the symmetry of the target states and a class of specific unitaries, we optimize the original verification strategy based on group theory. In this case, our new protocol can realize the efficient verification of three-qubit W class states.

Suggested Citation

  • Bao, Daipengwei & Liu, Min & Ou, Yangwei & Xu, Qingshan & Li, Qin & Tan, Xiaoqing, 2024. "Eigenvalue-based quantum state verification of three-qubit W class states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    • Handle: RePEc:eee:phsmap:v:639:y:2024:i:c:s0378437124001900
    DOI: 10.1016/j.physa.2024.129681
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    References listed on IDEAS

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    1. Yanli Zhou & Shican Liu & Tianhai Tian & Qi He & Xiangyu Ge, 2021. "Using Particle Swarm Optimization Algorithm to Calibrate the Term Structure Model," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-11, January.
    2. Marcus Cramer & Martin B. Plenio & Steven T. Flammia & Rolando Somma & David Gross & Stephen D. Bartlett & Olivier Landon-Cardinal & David Poulin & Yi-Kai Liu, 2010. "Efficient quantum state tomography," Nature Communications, Nature, vol. 1(1), pages 1-7, December.
    3. Andrea Coladangelo & Koon Tong Goh & Valerio Scarani, 2017. "All pure bipartite entangled states can be self-tested," Nature Communications, Nature, vol. 8(1), pages 1-5, August.
    4. Cao, Zhuo-Liang & Song, Wei, 2005. "Teleportation of a two-particle entangled state via W class states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 177-183.
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