Abstract
Perfect sharing of arbitrary single-qubit operation (PSASQO) with shared entanglements and LOCC is focused. A symmetric three-party PSASQO scheme is put forward by utilizing the five-qubit cluster state proposed by Briegel and Raussendorf (Phys Rev Lett 86:910, 2001). Some concrete discussions on the scheme are made, including its important features, the essential role of the quantum channel, its direct generalization to more-party cases, the problem of entanglement structure and its application perspective in some peculiar quantum scenario as well as its security analysis. Particularly, the experimental feasibilities of the scheme and its generalizations are demonstrated, i.e., showing the employed unitary operations are local and accessible single-qubit Pauli and two-qubit control NOT operations according to nowaday experimental techniques.
Similar content being viewed by others
References
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
Bohr, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48, 696 (1935)
Ekert, A.K.: Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bells theorem. Phys. Rev. Lett. 70, 1895 (1993)
Bennett, C.H., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 68, 557 (1992)
Cheung, C.Y., Zhang, Z.J.: Criterion for faithful teleportation with an arbitrary multiparticle channel. Phys. Rev. A 80, 022327 (2009)
Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)
Zhang, Z.J., Man, Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005)
Zhang, Z.J., Li, Y., Man, Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71, 044301 (2005)
Yan, F.L., Gao, T.: Quantum secret sharing between multiparty and multiparty without entanglement. Phys. Rev. A 72, 012304 (2005)
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, 042317 (2003)
Bennett, C.H., et al.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)
Pellizzari, T., Gardiner, S.A., Cirac, J.I., Zoller, P.: Decoherence, continuous observation, and quantum computing: a cavity QED model. Phys. Rev. Lett. 75, 3788 (1995)
Muralidharan, S., Panigrahi, P.K.: Quantum-information splitting using multipartite cluster states. Phys. Rev. A 78, 062333 (2008)
Paul, N., Menon, J.V., Karumanchi, S., Muralidharan, S., Panigrahi, P.K.: Quantum tasks using six qubit cluster states. Quantum Inf. Process. 10, 619 (2011)
Muralidharan, S., Jain, S., Panigrahi, P.K.: Splitting of quantum information using N-qubit linear cluster states. Opt. Commun. 284, 1082 (2011)
Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)
Bandyopadhyay, S.: Teleportation and secret sharing with pure entangled states. Phys. Rev. A 62, 012308 (2000)
Bagherinezhad, S., Karimipour, V.: Quantum secret sharing based on reusable Greenberger-Horne-Zeilinger states as secure carriers. Phys. Rev. A 67, 044302 (2003)
Huelga, S.F., Vaccaro, J.A., Chefles, A.: Quantum remote control: teleportation of unitary operations. Phys. Rev. A 63, 042303 (2001)
Zou, X.B., Pahlke, K., Mathis, W.: Teleportation implementation of nondeterministic quantum logic operations by using linear optical elements. Phys. Rev. A 65, 064305 (2002)
Dur, W., Vidal, G., Cirac, J.I.: Optimal conversion of nonlocal unitary operations. Phys. Rev. Lett. 89, 057901 (2002)
Zhang, Y.S., Ye, M.Y., Guo, G.C.: Conditions for optimal construction of two-qubit nonlocal gates. Phys. Rev. A 71, 062331 (2005)
Wang, A.M.: Remote implementations of partially unknown quantum operations of multiqubits. Phys. Rev. A 74, 032317 (2007)
Wang, A.M.: Combined and controlled remote implementations of partially unknown quantum operations of multiqubits using Greenberger-Horne-Zeilinger states. Phys. Rev. A 75, 062323 (2007)
Zhao, N.B., Wang, A.M.: Hybrid protocol of remote implementations of quantum operations. Phys. Rev. A 76, 062317 (2007)
Zhang, Z.J., Cheung, C.Y.: Shared quantum remote control: quantum operation sharing. J. Phys. B 44, 165508 (2011)
Ye, B.L., Liu, Y.M., Liu, X.S., Zhang, Z.J.: Remotely sharing single-qubit operation with five-qubit genuine state. Chin. Phys. Lett. 30, 020301 (2013)
Ji, Q.B., Liu, Y.M., Yin, X.F., Liu, X. S. Zhang, Z.J.: Quantum operation sharing with symmetric and asymmetric W states. Quantum inf. process. doi:10.1007/s11128-013-0533-9
Liu, D.C., Liu, Y.M., Liu, X.S., Zhang, Z.J.: Shared quantum control via sharing operation on remote single qutrit. Quantum, information processing (to be submitted)
Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910 (2001)
Gross, D., Kieling, K., Eisert, J.: Potential and limits to cluster-state quantum computing using probabilistic gates. Phys. Rev. A 74, 042343 (2006)
Bouwmeester, D., Pan, J.W., Mattle, K., et al.: Experimental quantum teleportation. Nature 390, 575 (1997)
Boschi, D., Branca, S., Martini, F.D., Hardy, L., Popescu, S.: Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80, 1121 (1998)
Riebe, M., et al.: Deterministic quantum teleportation with atoms. Nature 429, 734 (2004)
Barrett, M.D., et al.: Deterministic quantum teleportation of atomic qubits. Nature 429, 737 (2004)
Zuo, X.Q., Liu, Y.M., Xu, C.J., Zhang, Z.J.: Generalized tripartite scheme for sharing arbitrary 2\(n\)-qudit state. Opt. Commun. 283, 4108 (2010)
Zheng, S.B.: Scheme for approximate conditional teleportation of an unknown atomic state without the Bell-state measurement. Phys. Rev. A 69, 064302 (2004)
Acknowledgments
This work is supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20103401110007, the NNSFC under Grant Nos.10874122, 10975001, 51072002 and 51272003, the Program for Excellent Talents at the University of Guangdong province (Guangdong Teacher Letter [1010] No.79), and the 211 Project of Anhui University
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, S., Liu, Y., Chen, J. et al. Deterministic single-qubit operation sharing with five-qubit cluster state. Quantum Inf Process 12, 2497–2507 (2013). https://doi.org/10.1007/s11128-013-0537-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-013-0537-5