The structure of product bases of $\mathbb{C}^{2}\bigotimes\mathbb{C}^{n}$

Abstract

In this paper, we mainly characterize the structure of product bases of the complex vector space $\mathbb{C}^{2}\bigotimes\mathbb{C}^{n}$. It gives an answer to the conjecture in case of $d=2n$ proposed by McNulty et al in 2016. As the application of the result, we obtain all the product bases of a bipartite system $\mathbb{C}^{2}\bigotimes\mathbb{C}^{n}$. It is helpful to review the structure of all the product bases of $\mathbb{C}^{2}\bigotimes\mathbb{C}^{2}$ and $\mathbb{C}^{2}\bigotimes\mathbb{C}^{3}$, which given by McNulty et al.