# Separability Criterion for Multipartite Pure States

## TL;DR

This paper introduces new criteria for determining the separability of multipartite pure quantum states, including an efficient algorithm that does not require Schmidt decomposition, advancing the analysis of quantum entanglement.

## Contribution

The paper presents novel separability criteria and an algorithm that simplifies the process without needing Schmidt decomposition, improving the analysis of multipartite quantum states.

## Key findings

- Established a relationship between separability and Schmidt decomposability.
- Derived a criterion that does not require Schmidt decomposition.
- Provided an effective algorithm for separability judgment.

## Abstract

In this paper, we give out some effective criterions which can be used to judge the separability of multipartite pure states. We obtain the relationship between separability and Schmidt decomposable of multipartite pure states in Theorem1. The first criterion derived from Theorem2 dose not need the Schmidt decomposition which is hard to find for multipartite states. Theorem3 is more profound which can be used to deduce Corollary1 which is one of the main results in [1]. Finally, we give out an algorithm which can be used to judge the separability of multipartite pure states effectively.