中国物理B ›› 2024, Vol. 33 ›› Issue (8): 80304-080304.doi: 10.1088/1674-1056/ad47ae

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New construction of mutually unbiased bases for odd-dimensional state space

Chenghong Wang(王成红)1, Kun Wang(王昆)1, and Zhu-Jun Zheng(郑驻军)2,†   

  1. 1 College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
    2 School of Mathematics, South China University of Technology, Guangzhou 510641, China
  • 收稿日期:2024-02-02 修回日期:2024-04-13 出版日期:2024-08-15 发布日期:2024-07-15
  • 通讯作者: Zhu-Jun Zheng E-mail:zhengzj@scut.edu.cn
  • 基金资助:
    Project supported by Zhoukou Normal University, China, High Level Talents Research Start Funding Project (Grant No. ZKNUC2022010), Key Scientific Research Project of Henan Province (Grant No. 22B110022), Key Research and Development Project of Guangdong Province (Grant No. 2020B0303300001), and the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B1515310016).

New construction of mutually unbiased bases for odd-dimensional state space

Chenghong Wang(王成红)1, Kun Wang(王昆)1, and Zhu-Jun Zheng(郑驻军)2,†   

  1. 1 College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
    2 School of Mathematics, South China University of Technology, Guangzhou 510641, China
  • Received:2024-02-02 Revised:2024-04-13 Online:2024-08-15 Published:2024-07-15
  • Contact: Zhu-Jun Zheng E-mail:zhengzj@scut.edu.cn
  • Supported by:
    Project supported by Zhoukou Normal University, China, High Level Talents Research Start Funding Project (Grant No. ZKNUC2022010), Key Scientific Research Project of Henan Province (Grant No. 22B110022), Key Research and Development Project of Guangdong Province (Grant No. 2020B0303300001), and the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B1515310016).

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摘要： We study the construction of mutually unbiased bases in Hilbert space for composite dimensions $d$ which are not prime powers. We explore the results for composite dimensions which are true for prime power dimensions. We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases. In particular, we present four mutually unbiased bases in $\mathbb{C}^{15}$.

关键词: mutually unbiased bases, Hilbert space, Pauli matrix, quantum measurement

Abstract: We study the construction of mutually unbiased bases in Hilbert space for composite dimensions $d$ which are not prime powers. We explore the results for composite dimensions which are true for prime power dimensions. We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases. In particular, we present four mutually unbiased bases in $\mathbb{C}^{15}$.

Key words: mutually unbiased bases, Hilbert space, Pauli matrix, quantum measurement

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

  • 03.65.Aa
03.65.Ud (Entanglement and quantum nonlocality) 03.67.Hk (Quantum communication) 03.67.Mn (Entanglement measures, witnesses, and other characterizations)