Construct New Form of Maximally Nine-Qubit Entangled State Via Recurrence Relation
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Construct New Form of Maximally Nine-Qubit Entangled State Via Recurrence Relation Junling Che1
· Peilin Zhao1 · Feng Wen2
Received: 11 June 2020 / Accepted: 28 October 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Descrying all aspects of the quantum entanglement of multipartite quantum systems is an essential part when researching the quantum entanglement. Maximally multi-qubit entangled state is one of the research objects. Recently, attracted by a criterion for maximally entangled nine-qubit state and construct a nine-qubit maximally entangled state, we construct a new genuine maximally nine-qubit entangled state via the recurrence relation. Further, nine-qubit entangled state is found which can be seen as a new form maximally nine-qubit entangled state. There are 108 of purity equal to 1/16, 18 of purity equal to 1/8 in observation. We believe the result could provide a new idea for constructing more new maximally multi-qubit states. Keywords Recurrence relation · Maximally nine-qubit entangled state
1 Introduction For a long time, as an important theoretical component of quantum communication protocols, like quantum teleportation [1], quantum secure direct communication [2, 3], quantum key distribution [4, 5], and so on, quantum entanglement is a valuable resource. Recently, with rapid development of Quantum informatics [6–9], it is possible of more qubit entangle states achieved in the future. Due to its great relevance, from both the theoretical and practical points of view, it is imperative to explore and characterize all aspects of the quantum Junling Che
[email protected] Peilin Zhao [email protected] Feng Wen [email protected] 1
School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710061, China
2
Key Laboratory for Physical Electronics and Devices of the Ministry of Education, School of Science, Shaanxi Key Lab of Information Photonic Technique and Institute of Wide Bandgap Semiconductors, Xi’an Jiaotong University, Xi’an 710049, China
International Journal of Theoretical Physics
entanglement of multipartite quantum systems. A state has a large multipartite entanglement if its average bipartite entanglement is large. Maximally multi-qubit entangled state (MMES) [10], the state whose entanglement is maximal for every (balanced) bipartition, is a productive tool in quantum entanglement investigation. As a perfect entanglement resource in quantum communication and computing, an important portion of quantum information processing when dealing with many parties, maximally multi-qubit entangled state (MMES) has received much theoretical attention [11–14]. Using averaged purity of overall [n/2]-qubit subsystems reaches its minimum, recently, zha et al. [15] present a generalized criterion for maximally entangled nine-qubit state, whose minimum averaged subsystem purity should be equal to 1/14. They also construct a nine-qubit maximally entangled states of 110, 15 and 1 balanced purities equal to 1/16, 1/8 and 1/4, respectively. B
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