It is worth studying recurrence relation of multi-qubit states due to its benefits to the criterion and measurement of quantum entanglement. Recently, Huang et al. presented an expand recurrence relation of multi-qubit state. Using this expand recurrence relation and Brown state, we construct a new seven-qubit maximally entangled states of 32 and 3 balanced purities equal to 1/8 and 1/4, whose averaged subsystem purity is equal to 19/140. We found that the marginal density matrices for subsystems of 1 and 2 qubits all completely mixed in these states.

中文翻译：

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通过布朗态构造最大七量子位纠缠态

多量子位态的递推关系因其有利于量子纠缠的判据和测量而值得研究。最近，Huang等人。提出了多量子位状态的扩展递归关系。使用这个扩展递归关系和布朗态，我们构建了一个新的 7 量子位最大纠缠态，其 32 和 3 个平衡纯度等于 1/8 和 1/4，其平均子系统纯度等于 19/140。我们发现 1 和 2 量子位子系统的边际密度矩阵在这些状态下都完全混合。