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

TL;DR

This paper characterizes the structure of product bases in the bipartite space ^{2}^{n}, solving a conjecture for the case where the dimension is 2n and classifying all such bases.

Contribution

It provides a complete characterization of product bases in ^{2}^{n} and confirms a conjecture for the case d=2n, extending previous results for smaller systems.

Findings

All product bases of ^{2}^{n} are classified.

The conjecture by McNulty et al. is confirmed for d=2n.

Structural insights into product bases of bipartite systems.

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.