Mutually unbiased maximally entangled bases from difference matrices

• URL: http://arxiv.org/abs/2210.01517v1
• Date: Tue, 4 Oct 2022 10:45:22 GMT
• Title: Mutually unbiased maximally entangled bases from difference matrices
• Authors: Yajuan Zang, Zihong Tian, Hui-Juan Zuo, and Shao-Ming Fei
• Abstract summary: Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We establish $q$ mutually unbiased bases with $q-1$ maximally entangled bases and one product basis in $mathbbCqotimes mathbbCq$ for arbitrary prime power $q$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish $q$ mutually unbiased bases with $q-1$ maximally entangled bases and one product basis in $\mathbb{C}^q\otimes \mathbb{C}^q$ for arbitrary prime power $q$. In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in $\mathbb{C}^{12}\otimes \mathbb{C}^{12}$ and $\mathbb{C}^{21}\otimes\mathbb{C}^{21}$, which improve the known lower bounds for $d=3m$, with $(3,m)=1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we construct $p+1$ mutually unbiased bases with $p$ maximally entangled bases and one product basis in $\mathbb{C}^p\otimes \mathbb{C}^{p^2}$ for arbitrary prime number $p$.

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