Abstract
The exploration of quantum entanglement in multipartite quantum systems is of great significance to the study of quantum entanglement, maximally multi-qubit entangled state is one of the research objects. Recently, Che et al. presented a recurrence relation of multi-qubit state. According to this inspiration, we present the recurrence relation of maximally multi-qubit pure states of N-qubits for N = 6, 7, 8. Further, some new forms of the seven- and eight-qubit maximally entangled states are found with the recurrence relation.
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References
Bennett, C.H., Brassard, G., Crépeau, C., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)
Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)
Deng, F.G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)
Facchi, P., Florio, G., Parisi, G., et al.: Maximally multipartite entangled states. Phys. Rev. A 77(R), 060304 (2008)
Albeverio, S., Fei, S.M., Parashar, P., et al.: Nonlocal properties and local invariants for bipartite systems. Phys. Rev. A 68, 010303 (2003)
Borras, A., Plastino, A.R., Batle, J., et al.: Multiqubit systems: highly entangled states and entanglement distribution. Phys. A: Math. Theor 40, 13407 (2007)
De Vicente, J.I., Spee, C., Kraus, B.: The maximally entangled set of multipartite quantum states. Phys. Rev. Lett. 111, 110502 (2013)
Goyeneche, D., Bielawski, J., Zyczkowski, K.: Multipartite entanglement in heterogeneous systems. Phys. Rev. A 90, 22316 (2014)
Yuan, J.P., Dong, S.C., Wu, C.H., et al.: Optically tunable grating in a V plus Xi configuration involving a Rydberg state. Opt. Express 28, 23820 (2020)
Zhang, Z.Y., Liang, S., Li, F., et al.: Spin-orbit coupling in photonic graphene. Optica 7, 455 (2020)
Che, J.L., Zhang, Z.Y., Hu, M.L., et al.: Novel Rydberg eight-wave mixing process controlled in the nonlinear phase of a circularly polarized field. Opt. Express 26, 3024 (2018)
Che, J.L., Wu, H.: Construct multipartite maximally entangled state via recurrence relation. Int. J. Theor. Phys. 58, 584–590 (2019)
Zha, X.W., Yuan, C.Z., Zhang, Y.P.: Generalized criterion for a maximally multi-qubit entangled state. Laser Phys. Lett. 10, 45201 (2013)
Zha, X.W., Song, H.Y., Qi, J.X., et al.: A maximally entangled seven-qubit state. Phys. A Math. Theor 45, 25 (2012)
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Zhi, P., Hu, Y. The Recurrence Relation of Maximally Six-, Seven- and Eight-Qubit Entangled States. Int J Theor Phys 60, 2049–2053 (2021). https://doi.org/10.1007/s10773-021-04820-1
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DOI: https://doi.org/10.1007/s10773-021-04820-1