Controlled remote state preparation protocols via AKLT states

详细信息    查看全文

• 作者：Lin Lin Liu (1)
  Tzonelih Hwang (1)
  
• 关键词：AKLT state ; Controlled ; joint remote state preparation (CJRSP) ; Controlled remote state preparation (CRSP) ; Gapped ground state
• 刊名：Quantum Information Processing
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：13
• 期：7
• 页码：1639-1650
• 全文大小：
• 参考文献：1. Bennett, C.H., Shor, P.W.: Quantum information theory. IEEE Trans. Inf. Theory 44(6), 2724-742 (1998) CrossRef
  2. Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000) CrossRef
  3. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000) CrossRef
  4. Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87(7), 077902 (2001) CrossRef
  5. Dai, H.Y., Chen, P.X., Liang, L.M., Li, C.Z.: Classical communication cost and remote preparation of the four-particle GHZ class state. Phys. Lett. A 355, 285-88 (2006) CrossRef
  6. Wang, Z.Y., Liu, Y.M., Zuo, X.Q., Zhang, Z.J.: Controlled remote state preparation. Commun. Theor. Phys. (Beijing, China) 52(2), 235-40 (2009) CrossRef
  7. Guan, X.W., Chen, X.B., Yang, Y.X.: Controlled-joint remote preparation of an arbitrary two-qubit state via non-maximally entangled channel. Int. J. Theor. Phys. 51, 3575-586 (2012) CrossRef
  8. Wang, D., Ye, L.: Multi party-controlled joint remote preparation. Quantum Inf. process. 12, 3223-237 (2013) CrossRef
  9. Liu, J.M., Han, J.R., Wang, Y.Z.: Multiparticle generalization of remote state preparation. Commun. Theor. Phys. 42(2), 211-14 (2004)
  10. Ma, P.C., Zhan, Y.B.: Scheme for probabilistic remotely preparing a multi-particle entangled GHZ state. Chin. Phys. B 17(2), 445-50 (2008) CrossRef
  11. Ma, P.C., Zhan, Y.B.: Scheme for remotely preparing a four-particle entangled cluster-type state. Opt. Commun. 283, 2640-643 (2010) CrossRef
  12. Nguyen, B.A., Cao, T.B., Nung, V.D., Kim, J.: Remote state preparation with unit success probability. Adv. Nat. Sci.: Nanosci. Nanotechnol. 2, 035009 (2011)
  13. Nguyen, B.A.: Joint remote state preparation via W and W-type states. Opt. Commun. 283, 4113-117 (2010) CrossRef
  14. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Valence bond ground states in isotropic quantum antiferromagnets. Commun. Math. Phys 115, 477-28 (1988) CrossRef
  15. Chen, X., Zeng, B., Gu, Z.C., Yoshida, B., Chuang, I.L.: Gapped two-body hamiltonian whose unique ground state is universal for one-way quantum computation. Phys. Rev. Lett. 102, 220501 (2009) CrossRef
  16. Darmawan, A.S., Bartlett, S.D.: Optical spin-1 chain and its use as a quantum-computational wire. Phys. Rev. A 82, 012328 (2010) CrossRef
  17. Kaltenbaek, R., Lavoie, J., Zeng, B., Bartlett, S.D., Resch, K.J.: Optical one-way quantum computing with a simulated valence-bond solid. Nat. Phys. lett. 6, 850-54 (2010) CrossRef
  18. Coello, J.G., Bayat, A., Bose, S., Jefferson, J.H., Creffield, C.E.: Spin filtering and entanglement swapping through coherent evolution of a single quantum dot. Phys. Rev. Lett. 105, 080502 (2010) CrossRef
  19. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Rigorous results on valence-bond ground states in antiferromagnets. Phys. Rev. Lett. 59(7), 799-02 (1987) CrossRef
  20. Fan, H., Korepin, V., Roychowdhury, V.: Entanglement in a valence-bond solid state. Phys. Rev. Lett. 93, 227203 (2004) CrossRef
  21. Peng, J.Y., Luo, M.X., Mo, Z.W.: Joint remote state preparation of arbitrary two-particle states via GHZ-type states. Quantum Inf. Process. 12, 2325-342 (2013) CrossRef
  22. Wang, D., Ye, L.: Joint remote preparation of a class of four-qubit cluster-like states with tripartite entanglements and positive operator-valued measurements. Int. J. Theor. Phys. 52, 3075-085 (2013) CrossRef
  23. Chen, Q.Q., Xia, Y., Song, J., Nguyen, B.A.: Joint remote state preparation of a W-type state via W-type states. Phys. Lett. A 374, 4483-487 (2010) CrossRef
  24. Nguyen, B.A., Cao, T.B., Nung, V.D.: Deterministic joint remote state preparation. Phys. Lett. A 375, 3570-573 (2011) CrossRef
  25. Chen, Q.Q., Xia, Y., Nguyen, B.A.: Flexible deterministic joint remote state preparation with a passive receiver. Phys. Scr. 87, 025005 (2013) CrossRef
  26. Zhan, Y.B., Fu, H., Li, X.W., Ma, P.C.: Deterministic remote preparation of a four-qubit cluster-type entangled state. Int. J. Theor. Phys. 52, 2615-622 (2013) CrossRef
  27. Nielsen, M.A., Chuang, I.L.: Quantum Comput. Quantum Inf. Cambridge Univ. Press, Cambridge (2000)
  
• 作者单位：Lin Lin Liu (1)
  Tzonelih Hwang (1)
  
  1. Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan?, 70101, Taiwan
  
• ISSN：1573-1332

文摘

In this paper, we proposed two controlled remote state preparation of an arbitrary single-qubit state schemes one for deterministic controlled remote state preparation the other for probabilistic controlled-joint remote state preparation with 2/3 probability. Both of them used the Affleck–Kennedy–Lieb–Tasaki (AKLT) state which consisted of bulk spin-1’s and two spin-1 \(/\) 2’s at the ends. Up to now, no RSP protocols using AKLT gapped ground states as a shared quantum resource had been presented thus far and Fan et al. showed the other AKLT property was that if we performed a Bell measurement on bulk, then a maximally entangled state would be shared by two ends. We utilized these properties to develop our controlled protocols.