The inseparability criterion provides a straightforward and efficient method for identifying and quantifying two-mode Gaussian quantum entanglement, making it a crucial tool in quantum optics experiments. However, it is crucial to recognize that the inseparability criterion serves only as a sufficient condition for entanglement assessment, thereby posing a risk of missed detection during evaluation. This paper investigates the use of the inseparability criterion in assessing two-mode squeezed states, with a particular focus on examining missed entanglement detection due to entanglement asymmetry. The results show that when decoherence symmetrically affects both modes, the inseparability criterion effectively detects entanglement. In contrast, when this symmetry is broken, the criterion may fail to identify entanglement, with the likelihood of missed detection increasing with increasing asymmetry. By comparing these results with the positive partial transpose criterion, which serves as a necessary and sufficient condition, the occurrence of missed detections by the inseparability criterion is confirmed. Our research not only provides valuable insights into the application of the inseparability criterion in quantum information tasks but also deepens the understanding of its operational principles and limitations.

本文介绍了一种用于里德伯原子激发的纳秒脉冲激光系统。实验利用两个kHz线宽的1018nm连续激光器作为种子源，通过两个20GHz带宽的光纤调制器产生时间分离的脉冲激光；脉冲激光经掺镱光纤放大器后输出峰值功率约4600W，单次穿过PPLN晶体倍频获得509nm脉冲激光，典型脉冲激光峰值功率约173W。该激光系统单路输出脉冲重复频率在300 kHz-100MHz范围连续可调，脉宽在1ns-100 ns范围连续可调。该509nm激光在聚焦条件下可以实现GHz带宽的铯原子里德伯态激发。

The inseparability criterion provides a straightforward and efficient method for identifying and quantifying two-mode Gaussian quantum entanglement, making it a crucial tool in quantum optics experiments. However, it is crucial to recognize that the inseparability criterion serves only as a sufficient condition for entanglement assessment, thereby posing a risk of missed detection during evaluation. This paper investigates the use of the inseparability criterion in assessing two-mode squeezed states, with a particular focus on examining missed entanglement detection due to entanglement asymmetry. The results show that when decoherence symmetrically affects both modes, the inseparability criterion effectively detects entanglement. In contrast, when this symmetry is broken, the criterion may fail to identify entanglement, with the likelihood of missed detection increasing alongside rising asymmetry. By comparing these results with the positive partial transpose criterion, which serves as a necessary and sufficient condition, the occurrence of missed detections by the inseparability criterion is confirmed. Our research not only provide valuable insights into the application of the inseparability criterion in quantum information tasks but also deepens the understanding of its operational principles and limitations.