Abstract
Recently, Bich et al. (Int. J. Theor. Phys. 51: 2272, 2012) proposed two deterministic joint remote state preparation (JRSP) protocols of an arbitrary single-qubit state: one is for two preparers to remotely prepare for a receiver by using two Einstein-Podolsky-Rosen (ERP) pairs; the other is its generalized form in the case of arbitrary N (N > 2) preparers via N ERP pairs. While examining these two protocols, we find that the success probability for the receiver achieving the desired state is not deterministic, i.e., \(P^{N>2}_{suc}<1\), for N > 2 preparers in the second protocol. Through constructing two sets of adaptive projective measurement bases for both the real space and the complex space, an improved deterministic N-to-one JRSP protocol for an arbitrary single-qubit state is presented. Analysis shows our protocol can truly achieve the unit success probability, i.e., \(P^{N\geq 2}_{suc}=1\). What is more, the receiver can be randomly assigned even after the distribution of the qubits of EPR pairs, so it is more flexible and applicable in the network situation.
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Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 10–12 December 1984, pp. 175–179. IEEE Press, New York (1984)
Bennett, C.H.: Quantum cryptography Using any Two Nonorthogonal States. Phys. Rev. Lett 68(21), 3121–3124 (1992). doi:10.1103/PhysRevLett.68.3121
Yang, J., Xu, B.J., Guo, H.: Source monitoring for continuous-variable quantum key distribution. Phys. Rev. A 86(4), 042314 (2012). doi:10.1103/PhysRevA.86.042314
Cleve, R., Gottesman, D., Lo, H.K.: How to Share a quantum secret. Phys. Rev. Lett 83(3), 648–651 (1999). doi:10.1103/PhysRevLett.83.648
Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829–1834 (1999). doi:10.1103/PhysRevA.59.1829
Wang, H.B., Huang, Y.G., Fang, X., Gu, B., Fu, D.S.: High-capacity three-party quantum secret sharing with single photons in both the polarization and the spatial-mode degrees of freedom. Int. J. Theor. Phys. 52(4), 1043–1051 (2013). doi:10.1007/s10773-012-1418-x
Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68(4), 042317 (2003). doi:10.1103/PhysRevA.68.042317
Liu, W.J., Chen, H.W., Li, Z.Q., Liu, Z.H.: Efficient quantum secure direct communication with authentication. Chin. Phys. Lett 25(7), 2354–2357 (2008). doi:10.1088/0256-307X/25/7/007
Liu, W.J., Chen, H.W., Ma, T.H., Li, Z.Q., Liu, Z.H., Hu, W.B.: An efficient deterministic secure quantum communication scheme based on cluster states and identity authentication. Chinese. Phys. B 18(10), 4105–4109 (2009). doi:10.1088/1674-1056/18/10/007
Bennett, C.H., Brassard, G., Crpeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett 70(13), 1895–1899 (1993). doi:10.1103/PhysRevLett.70.1895
Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390(6660), 575–579 (1997). doi:10.1038/37539
Long, L.R., Li, H.W., Zhou, P., Fan, C., Yin, C.L.: Multiparty-controlled teleportation of an arbitrary GHZ-class state by using a D-dimensional (N+2)-particle nonmaximally entangled state as the quantum channel. SCI. China. Phys. Mech. 54(3), 484–490 (2011). doi:10.1007/s11433-011-4246
Liu, W.-J., Liu, C., Liu, Z.-H., Liu, J.-F., Geng, H.-T.: Same initial states attack in Yang et al.s quantum private comparison protocol and the improvement. Int. J. Theor. Phys. 53(1), 271–276 (2013). doi:10.1007/s10773-013-1807-9
Liu, W.J., Liu, C., Wang, H.B., Jia, T.T.: Quantum private comparison: a review. IETE Tech. Rev. 30(5) 439–445 (2013). doi:10.1007/s10773-013-1807-9
Huang, W., Wen, Q.Y., Liu, B., Gao, F., Sun, Y.: Robust and efficient quantum private comparison of equality with collective detection over collective-noise channels. SCI. China. Phys. Mech. 56(9), 1670–1678 (2013). doi:10.1007/s11433-013-5224-0
Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63(1), 014302 (2000)
Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 7, 077902 (2001)
Lo, H.-K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62(1), 2000
Xia, Y., Song, J., Song, H.S.: Multiparty remote state preparation. J. Phys. B At. Mol. Opt. Phys. 40(18), 3719–3724 (2007). doi:10.1088/0953-4075/40/18/011
An, N.B., Kim, J.: Collective remote state preparation. Int. J. Quantum Inf. 6(5), 1051–1066 (2008). doi:10.1142/s0219749908004304
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(44), 4483–4487 (2010). doi:10.1016/j.physleta.2010.09.013
Luo, M.X., Chen, X.B., Ma, S.Y., Niu, X.X., Yang, Y.X.: Joint remote preparation of an arbitrary threequbit state. Opt. Commun. 283(23), 4796–4801 (2010). doi:10.1016/j.optcom.2010.07.043
Nguyen, B.A.: Joint remote preparation of a general two-qubit state. J. Phys. B At. Mol. Opt. Phys. 42(12), 125501 (2009). doi:10.1088/0953-4075/42/12/125501
Nguyen, B.A.: Joint remote state preparation via W and W-type states. Opt. Commun. 283(20), 4113–4117 (2010). doi:10.1016/j.optcom.2010.06.016
Xia, Y., Song, J., Song, H.S., Guo, J.L.: Multiparty remote state preparation with linear optical elements. Int. J. Quantum Inf. 6(5), 1127–1134 (2008). doi:10.1142/s0219749908004328
Xiao, X.-Q., Liu, J.-M., Zeng, G.: Joint remote state preparation of arbitrary two-and three-qubit states. J. Phys. B: At. Mol. Opt. Phys. 44(7), 075501 (2011). doi:10.1088/0953-075/44/7/075501
An, N.B., Bich, C.T., Van Don, N.: Deterministic joint Remote State Preparation. Phys. Lett. A 375(41), 3570–3573 (2011). doi:10.1016/j.physleta.2011.08.045
Xia, Y., Chen, Q.-Q., An, N.B.: Deterministic joint remote preparation of an arbitrary three-qubit state via Einstein-Podolsky-Rosen pairs with a passive receiver. J. Phys. A: Math. Theor. 45(33), 335306 (2012). doi:10.1088/1751-8113/45/33/335306
Yuan, W., Xin, J.: Deterministic joint remote state preparation of arbitrary two-and three-qubit states. Chinese. Phys. B 22(2), 020306 (2013). doi:10.1088/1674-056/22/2/020306
Ming-Ming, W., Xiu-Bo, C., Yi-Xian, Y.: Deterministic joint remote preparation of an arbitrary two-qubit state using the cluster state. Commun. Theor. Phys. 59(5), 568 (2013). doi:10.1088/0253-6102/59/5/09
Bich, C.T., Don, N.V., An, N.B.: Deterministic joint remote preparation of an arbitrary qubit via Einstein-Podolsky-Rosen pairs. Int. J. Theor. Phys. 51(7), 2272–2281 (2012). doi:10.1007/s10773-012-1107-9
Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press (2010)
Segal, I.E.: Postulates for general quantum mechanics. Ann. Math. 48(4), 930–948 (1947)
Acknowledgments
This work is supported by the National Nature Science Foundation of China (Grant Nos. 61103235, 61170321, 61373016 and 61373131), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), the State Key Laboratory of Software Engineering, Wuhan University(SKLSE2012-09-41), and the Practice Inovation Trainng Program Projects for the Jiangsu College Students (201310300018Z).
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Liu, WJ., Chen, ZF., Liu, C. et al. Improved Deterministic N-To-One Joint Remote Preparation of an Arbitrary Qubit via EPR Pairs. Int J Theor Phys 54, 472–483 (2015). https://doi.org/10.1007/s10773-014-2241-3
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DOI: https://doi.org/10.1007/s10773-014-2241-3