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

Abstract

In this paper, we mainly characterize the structure of product bases of the complex vector space ${\mathbb{C}}^2⨂{\mathbb{C}}^n$. 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 ${\mathbb{C}}^2⨂{\mathbb{C}}^n$. It is helpful to review the structure of all the product bases of ${\mathbb{C}}^2⨂{\mathbb{C}}^2$ and ${\mathbb{C}}^2⨂{\mathbb{C}}^3$, which given by McNulty et al.

10 pages