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

doi:10.1088/1674-1056/ad47ae

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 $\mathbb{C}^{15}$.

Keywords: mutually unbiased bases Hilbert space Pauli matrix quantum measurement

Received: 02 February 2024
Revised: 13 April 2024
Accepted manuscript online: 06 May 2024

PACS:	03.65.Aa	(Quantum systems with finite Hilbert space)
	03.65.Ud	(Entanglement and quantum nonlocality)
	03.67.Hk	(Quantum communication)
	03.67.Mn	(Entanglement measures, witnesses, and other characterizations)

Fund: 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).

Corresponding Authors: Zhu-Jun Zheng
E-mail: zhengzj@scut.edu.cn

Cite this article:

Chenghong Wang(王成红), Kun Wang(王昆), and Zhu-Jun Zheng(郑驻军) New construction of mutually unbiased bases for odd-dimensional state space 2024 Chin. Phys. B 33 080304

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