Abstract
Multi-qubit pure states play an important role in the application of quantum entanglement. In this paper, we find that the maximally multi-qubit pure states have a simple recurrence relation. The existence recurrence relation of multi-qubit maximally pure states of N-qubit for N = 2,3,⋯ ,8 are demonstrated. Further, some new characterizations of the multipartite maximally entangled states are found with the recurrence relation. These results may open a new window for constructing maximally multi-qubit states.
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