Detecting genuine multipartite entanglement based on a class of symmetric measurements

Quantum entanglement, a fundamental phenomenon in quantum mechanics, is crucial for various quantum technologies, including quantum teleportation, quantum key distribution, and quantum cryptography. Detecting genuine multipartite entanglement (GME) in complex quantum systems remains a challenging task due to the increasing complexity of multipartite systems. This article addresses this challenge by introducing a class of symmetric measurements, known as (N, M)-POVMs, which offer a broader range of measurement choices and advantages in information extraction and noise resistance. The authors derive concrete representations for quantum states in bipartite and tripartite systems using (N, M)-POVMs and propose novel criteria for detecting partial separability and GME in tripartite and four-partite systems. Through illustrative examples, the article demonstrates that these criteria are more efficient than existing ones, providing new insights into detecting genuine multipartite quantum entanglement. The findings could also be applied to the detection of other types of quantum correlations, making this article a valuable contribution to the field of quantum information science.