论文标题
从差异矩阵中互无偏的最大纠缠碱基
Mutually unbiased maximally entangled bases from difference matrices
论文作者
论文摘要
基于最大纠缠状态，我们探索了双方量子系统中相互无偏基的结构。我们提出了一种通过组合设计理论中的差异矩阵来构建互无偏基的新方法。特别是，我们建立了$ q $互公正的基础，并用$ q-1 $最大纠缠的基础和一个产品基础，以$ \ mathbb {c}^q \ otimes \ otimes \ mathbb {c}^q $ for nutary Prime Power $ q $。此外，我们构造了最大纠缠的基础，以构建非prime功率的复合数量的维度，例如$ \ Mathbb {C}^{12} \ otimes \ Mathbb {C}^c}^{C}^{12}^{12} $和$ \ MATHBB {C}^21}^$ aimime \ Mathbb {c}^{C}^21} {c {c 21}以$ d = 3m $的价格改善已知的下限，其中$（3，m）= 1 $ in $ \ mathbb {c}^{d} {d} \ otimes \ Mathbb {c}^{d} $。此外，我们用$ p $最大纠缠的基础构建$ p+1 $相互无偏基的基础，而在$ \ mathbb {c}^p \ otimes \ m athbb {c}^c}^{p^2} $中，用于任意质量数字$ p $。
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 $p$.
