中国物理B ›› 2023, Vol. 32 ›› Issue (5): 50302-050302.doi: 10.1088/1674-1056/acb9f1

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Bounds on positive operator-valued measure based coherence of superposition

Meng-Li Guo(郭梦丽)1, Jin-Min Liang(梁津敏)1, Bo Li(李波)2, Shao-Ming Fei(费少明)1,3,†, and Zhi-Xi Wang(王志玺)1,‡   

  1. 1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
    2 School of Computer and Computing Science, Hangzhou City University, Hangzhou 310015, China;
    3 Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
  • 收稿日期:2022-11-20 修回日期:2023-01-31 接受日期:2023-02-08 出版日期:2023-04-21 发布日期:2023-04-26
  • 通讯作者: Shao-Ming Fei, Zhi-Xi Wang E-mail:feishm@cnu.edu.cn;wangzhx@cnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12075159, 12171044, and 12175147), the Natural Science Foundation of Beijing (Grant No. Z190005), the Academician Innovation Platform of Hainan Province, Shenzhen Institute for Quantum Science and Engineering, and Southern University of Science and Technology (Grant No. SIQSE202001).

Bounds on positive operator-valued measure based coherence of superposition

Meng-Li Guo(郭梦丽)1, Jin-Min Liang(梁津敏)1, Bo Li(李波)2, Shao-Ming Fei(费少明)1,3,†, and Zhi-Xi Wang(王志玺)1,‡   

  1. 1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
    2 School of Computer and Computing Science, Hangzhou City University, Hangzhou 310015, China;
    3 Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
  • Received:2022-11-20 Revised:2023-01-31 Accepted:2023-02-08 Online:2023-04-21 Published:2023-04-26
  • Contact: Shao-Ming Fei, Zhi-Xi Wang E-mail:feishm@cnu.edu.cn;wangzhx@cnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12075159, 12171044, and 12175147), the Natural Science Foundation of Beijing (Grant No. Z190005), the Academician Innovation Platform of Hainan Province, Shenzhen Institute for Quantum Science and Engineering, and Southern University of Science and Technology (Grant No. SIQSE202001).

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摘要： Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the l1 norm of coherence, the robustness of coherence and the Tsallis relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition. Our results can be used to estimate range of quantum coherence of superposed states. Detailed examples are presented to verify our analytical bounds.

关键词: coherence, POVM-based coherence, relative entropy, l1 norm, Tsallis relative entropy

Abstract: Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the l1 norm of coherence, the robustness of coherence and the Tsallis relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition. Our results can be used to estimate range of quantum coherence of superposed states. Detailed examples are presented to verify our analytical bounds.

Key words: coherence, POVM-based coherence, relative entropy, l1 norm, Tsallis relative entropy

中图分类号:  (Quantum systems with finite Hilbert space)

  • 03.65.Aa
03.67.-a (Quantum information) 03.67.Mn (Entanglement measures, witnesses, and other characterizations)