# Construction of genuine multipartite entangled states

## TL;DR

This paper introduces a new method using the Kronecker product to systematically construct genuine multipartite entangled states, enhancing the ability to generate complex entanglement structures in quantum information.

## Contribution

It proposes a novel product based on the Kronecker product to construct genuine multipartite entangled states and analyzes its entanglement properties.

## Key findings

- The proposed product can produce genuine multipartite entangled states in specific cases.
- The entanglement of the Kronecker product is characterized and better understood.
- Provides a systematic approach for constructing multipartite entangled states.

## Abstract

Genuine multipartite entanglement is of great importance in quantum information, especially from the experimental point of view. Nevertheless, it is difficult to construct genuine multipartite entangled states systematically, because the genuine multipartite entanglement is unruly. We propose another product based on the Kronecker product in this paper. The Kronecker product is a common product in quantum information with good physical interpretation. We mainly investigate whether the proposed product of two genuine multipartite entangled states is still a genuine entangled one. We understand the entanglement of the proposed product better by characterizing the entanglement of the Kronecker product. Then we show the proposed product is a genuine multipartite entangled state in two cases. The results provide a systematical method to construct genuine multipartite entangled states of more parties.