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Quantizing multi-qubit entanglement is important for quantum information processing communication. In this paper, we study the relations between concurrence and purity of multi-qubit of pure states through detail calculation. For the maximally entangled states, we find that the averaged purity reaches its minimum; the concurrence reaches its maximum. Such results can be applied in quantizing multi-qubit entanglement. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In a recent paper (Zha et al. Laser Phys. Lett. 10, 045201, 2013), presented a criterion of maximally mutiqubit entangled states (MMES). Though there are several known examples of maximally entangled quantum states of two, three, five and six qubits, the mathematical structure for multi-qubit entanglement of more than seven qubits is less clear. With an emphasis on eight qubits, by this criterion, two new forms of maximally eight-qubit MMES is obtained, where the subsystems of 1, 2, and 3-qubits are all completely mixed. We believe that the new form eight-qubit maximally entangled state can play an important role in quantum information. [ABSTRACT FROM AUTHOR]