中国物理B ›› 2026, Vol. 35 ›› Issue (2): 20301-020301.doi: 10.1088/1674-1056/adf4b1

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Rigorous verification of quantum contextuality from anomalous weak value

Wei-Qian Zhao(赵炜谦)1, Si-Nan Pang(庞斯楠)1, Zi-Fu Su(苏子富)1, Tian-Ming Zhao(赵天明)2, Jin-Dong Wang(王金东)2,4, and Ya-Fei Yu(於亚飞)1,3,†   

  1. 1 Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510006, China;
    2 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China;
    3 Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen-Hong Kong International Science and Technology Park, Shenzhen 518109, China;
    4 Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, South China Normal University, Guangzhou 510006, China
  • 收稿日期:2025-06-19 修回日期:2025-07-19 接受日期:2025-07-28 发布日期:2026-02-09
  • 通讯作者: Ya-Fei Yu E-mail:yuyafei@m.scnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 62371199 and 62071186), the Natural Science Foundation of Guangdong Province, China (Grant No. 2024A1515012427), the Quantum Science Strategic Initiative Project of Guangdong Province, China (Grant No. GDZX2305001), and the Key Laboratory Project of Guangdong Province, China (Grant No. 2020B1212060066).

Rigorous verification of quantum contextuality from anomalous weak value

Wei-Qian Zhao(赵炜谦)1, Si-Nan Pang(庞斯楠)1, Zi-Fu Su(苏子富)1, Tian-Ming Zhao(赵天明)2, Jin-Dong Wang(王金东)2,4, and Ya-Fei Yu(於亚飞)1,3,†   

  1. 1 Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510006, China;
    2 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China;
    3 Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen-Hong Kong International Science and Technology Park, Shenzhen 518109, China;
    4 Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, South China Normal University, Guangzhou 510006, China
  • Received:2025-06-19 Revised:2025-07-19 Accepted:2025-07-28 Published:2026-02-09
  • Contact: Ya-Fei Yu E-mail:yuyafei@m.scnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 62371199 and 62071186), the Natural Science Foundation of Guangdong Province, China (Grant No. 2024A1515012427), the Quantum Science Strategic Initiative Project of Guangdong Province, China (Grant No. GDZX2305001), and the Key Laboratory Project of Guangdong Province, China (Grant No. 2020B1212060066).

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摘要： Weak measurement offers a powerful framework for probing nonclassical features of quantum mechanics, with anomalous weak values serving as operational signatures of contextuality. While the anomalous weak value verification of quantum contextuality has been predominantly investigated in the single-photon regime and analyzed under approximation condition of infinitesimally small perturbation strength. This study releases the approximation condition and takes into account the impact of perturbation strength on the rigor of the verification. And the investigation on the verification of contextuality is extended to the multi-photon scenarios for observing the influence of the correlation between photons on the verification. Without the limitation of infinitesimally small probability of disturbance, anomalous weak values are identified as necessary for contextuality to emerge, thereby refining the criterion proposed by Pusey [Phys. Rev. Lett. 113 200401 (2014)]. In the multi-photon scenarios, the emergence of contextuality also depends strongly on both the photon number and the photon-number distribution state. In particular, contextuality is found to be maximized when the single-photon component dominates and the second-order correlation is lower. These results highlight the critical role of photon statistics in experimental tests of contextuality via anomalous weak values.

关键词: quantum measurement, contextuality, weak measurement, weak values

Abstract: Weak measurement offers a powerful framework for probing nonclassical features of quantum mechanics, with anomalous weak values serving as operational signatures of contextuality. While the anomalous weak value verification of quantum contextuality has been predominantly investigated in the single-photon regime and analyzed under approximation condition of infinitesimally small perturbation strength. This study releases the approximation condition and takes into account the impact of perturbation strength on the rigor of the verification. And the investigation on the verification of contextuality is extended to the multi-photon scenarios for observing the influence of the correlation between photons on the verification. Without the limitation of infinitesimally small probability of disturbance, anomalous weak values are identified as necessary for contextuality to emerge, thereby refining the criterion proposed by Pusey [Phys. Rev. Lett. 113 200401 (2014)]. In the multi-photon scenarios, the emergence of contextuality also depends strongly on both the photon number and the photon-number distribution state. In particular, contextuality is found to be maximized when the single-photon component dominates and the second-order correlation is lower. These results highlight the critical role of photon statistics in experimental tests of contextuality via anomalous weak values.

Key words: quantum measurement, contextuality, weak measurement, weak values

中图分类号:  (Foundations of quantum mechanics; measurement theory)

  • 03.65.Ta
03.67.-a (Quantum information) 42.50.-p (Quantum optics) 42.50.Xa (Optical tests of quantum theory)