Efficient detection for quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems

TL;DR

This paper introduces practical criteria for detecting quantum states with fewer than $k$ unentangled particles in multipartite systems, improving detection capabilities over existing methods.

Contribution

The authors develop new operator-based criteria for identifying such quantum states, demonstrating their effectiveness through concrete examples.

Findings

Effective detection of quantum states with fewer than $k$ unentangled particles.

Our criteria outperform existing methods in certain cases.

Validated through specific quantum state examples.

Abstract

In this paper, we mainly investigate the detection of quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems. Based on calculations about operators, we derive two practical criteria for judging $N$-partite quantum states owning fewer than $k$ unentangled particles. In addition, we demonstrate the effectiveness of our frameworks through some concrete examples, and specifically point out the quantum states having fewer than $k$ unentangled particles that our methods can detect, while other criteria cannot recognize.