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International Journal of Theoretical Physics

Construct New Form of Maximally Nine-Qubit Entangled State Via Recurrence Relation

Junling Che, Peilin Zhao, Feng Wen

Published Nov 5, 2020• 4 citations
Publisher
DOI
10.1007/s10773-020-04648-1

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Abstract The notion of a maximally entangled state depends on the measure used to give rise to a rich envision of multipartite state. Recently, Che et al presented a recurrence relation of multi-qubit states. According to this inspiration, we present an expanded recurrence relation of the maximally multipartite state. Using this expanded recurrence relation and Bell state, some new forms of the maximally four-, six-, eight-qubits states are presented. The construct of the maximally multipartite state through recurrence relationships is of great potential.
Different mathematics forms of entangled state can judge prepared many particles is if entangled. Entangled state is a key role of quantum information technology. The more entangled states are generated, the better performances are presented. In order to make it more convenient to generate entangled state or judge the state prepared is entangled, we investigate three-qubit GHZ state and expand recurrence relation based on an expand recurrence relation of multi-qubit state. Furthermore, new forms of maximally five and seven-qubit entangled states are reconstructed via three-qubit GHZ state. These new forms stand for universal law of n-qubit and [Formula: see text]-qubit can have direct application in quantum entangle state generation and quantum communications.
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.