Huber et al. [Phys. Rev. Lett. 118 (2017) 200502] have proved that a seven-qubit state whose three-body marginal states are all maximally mixed does not exist. Here, we propose a method to build a maximally entangled state based on orthogonal arrays to construct maximally entangled seven-qubit states. Using this method, we not only determine that a seven-qubit state whose three-body marginals are all maximally mixed does not exist, but also find the condition for maximally entangled seven-qubit states. We consider that π ME = 19/140 is a condition for maximally entangled seven-qubit states. Furthermore, we derive three forms of maximally entangled seven-qubit states via orthogonal arrays.

中文翻译：

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通过正交阵列构造最大纠缠的七比特状态

Huber等。[物理 牧师 118（2017）200502]已证明不存在三体边际状态都被最大混合的七量子位状态。在这里，我们提出了一种基于正交数组构造最大纠缠态的方法，以构造最大纠缠七比特态。使用这种方法，我们不仅确定不存在三体边际都被最大混合的七量子位状态，而且还找到了最大纠缠的七量子位状态的条件。我们认为πME = 19/140是最大纠缠七比特状态的条件。此外，我们通过正交阵列得出三种形式的最大纠缠七比特态。