In quantum many-body systems, W class states are typical examples of states with genuine multipartite entanglement. They have been found to be valuable resources in many quantum information processing tasks. However, the characterization and verification of W class states still remains an intractable problem. Here we first propose an eigenvalue-based verification protocol consisting of four practical adaptive local projective measurement tests, and obtain the optimal test probabilities with particle swarm optimization algorithm. The efficiency achieved by this protocol is far from satisfactory when compared with the theoretical upper bound. Then by utilizing the symmetry of the target states and a class of specific unitaries, we optimize the original verification strategy based on group theory. In this case, our new protocol can realize the efficient verification of three-qubit W class states.

中文翻译：

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基于特征值的三量子位 W 类态量子态验证

在量子多体系统中，W类态是真正多体纠缠态的典型例子。人们发现它们是许多量子信息处理任务中的宝贵资源。然而，W类状态的表征和验证仍然是一个棘手的问题。在这里，我们首先提出一种基于特征值的验证协议，由四个实用的自适应局部投影测量测试组成，并通过粒子群优化算法获得最佳测试概率。与理论上限相比，该协议所实现的效率远不能令人满意。然后利用目标态的对称性和一类特定酉性，优化了原有的基于群论的验证策略。在这种情况下，我们的新协议可以实现三量子位W类状态的高效验证。