Abstract
Quantum walks have emerged as an interesting approach to implementing quantum information processing task in recent years. In this work, we take advantage of the properties of quantum walks to design a novel kind of flexible and conclusive quantum teleportation scheme of multiple arbitrary qubits. First, two-walker quantum walks on three types of quantum structures, the line, the cycle and two-vertice complete graph with loops, are utilized to accomplish the teleportation of an arbitrary 2-qubit state. Second, without loss of generality, a generalization for teleporting an arbitrary N-qubit state is also shown by N-walker quantum walks on two-vertice complete graph with loops. Our scheme has two merits. (i) Three different quantum-walk structures can be used to teleport an arbitrary N-qubit state, which means that one can implement the scheme flexibly, depending on the concrete experimental environment. (ii) The prior entangled state is not necessarily prepared, as multiple-walker quantum walks may contain entanglement. In addition, the single-particle projective measurement and single-qubit gate are required, rather than a joint measurement and controlled-NOT gate, which will possibly simplify experimental realizations of this scheme. This work stimulates us to explore more potential applications of multi-walker quantum walks.
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References
Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48(2), 1687 (1993)
Childs, A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102(18), 180501 (2009)
Lovett, N.B., Cooper, S., Everitt, M., Trevers, M., Kendon, V.: Universal quantum computation using the discrete-time quantum walk. Phys. Rev. A 81(4), 042330 (2010)
Childs, A.M., Gosset, D., Webb, Z.: Universal computation by multiparticle quantum walk. Science 339(6121), 791 (2013)
Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67(5), 052307 (2003)
Ambainis, A., Kempe, J., Rivosh, A.: In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1099–1108. Society for Industrial and Applied Mathematics (2005)
Tulsi, A.: Faster quantum-walk algorithm for the two-dimensional spatial search. Phys. Rev. A 78(1), 012310 (2008)
Perets, H.B., Lahini, Y., Pozzi, F., Sorel, M., Morandotti, R., Silberberg, Y.: Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100(17), 170506 (2008)
Xue, P., Sanders, B.C., Leibfried, D.: Quantum walk on a line for a trapped ion. Phys. Rev. Lett. 103(18), 183602 (2009)
Goyal, S.K., Roux, F.S., Forbes, A., Konrad, T.: Implementing quantum walks using orbital angular momentum of classical light. Phys. Rev. Lett. 110(26), 263602 (2013)
Xue, P., Zhang, R., Qin, H., Zhan, X., Bian, Z., Li, J., Sanders, B.C.: Experimental quantum-walk revival with a time-dependent coin. Phys. Rev. Lett. 114(14), 140502 (2015)
Farhi, E., Gutmann, S.: Quantum computation and decision trees. Phys. Rev. A 58(2), 915 (1998)
Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 44(4), 307 (2003)
Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., Watrous, J.: In: Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computing ACM, pp. 37–49 (2001)
Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: In: Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computing ACM, pp. 50–59 (2001)
Bednarska, M., Grudka, A., Kurzyński, P., Łuczak, T., Wójcik, A.: Quantum walks on cycles. Phys. Lett. A 317(1–2), 21 (2003)
Carneiro, I., Loo, M., Xu, X., Girerd, M., Kendon, V., Knight, P.L.: Entanglement in coined quantum walks on regular graphs. New J. Phys. 7(1), 156 (2005)
Orthey, A.C., Amorim, E.P.: Asymptotic entanglement in quantum walks from delocalized initial states. Quantum Inf. Process. 16(9), 224 (2017)
Linden, N., Sharam, J.: Inhomogeneous quantum walks. Phys. Rev. A 80(5), 052327 (2009)
Kurzyński, P., Wójcik, A.: Discrete-time quantum walk approach to state transfer. Phys. Rev. A 83(6), 062315 (2011)
Konno, N., Łuczak, T., Segawa, E.: Limit measures of inhomogeneous discrete-time quantum walks in one dimension. Quantum Inf. Process. 12(1), 33 (2013)
Zhang, R., Xue, P., Twamley, J.: One-dimensional quantum walks with single-point phase defects. Phys. Rev. A 89(4), 042317 (2014)
Suzuki, A.: Asymptotic velocity of a position-dependent quantum walk. Quantum Inf. Process. 15(1), 103 (2016)
Ribeiro, P., Milman, P., Mosseri, R.: Aperiodic quantum random walks. Phys. Rev. Lett. 93(19), 190503 (2004)
Banuls, M., Navarrete, C., Pérez, A., Roldán, E., Soriano, J.: Quantum walk with a time-dependent coin. Phys. Rev. A 73(6), 062304 (2006)
Montero, M.: Invariance in quantum walks with time-dependent coin operators. Phys. Rev. A 90(6), 062312 (2014)
Kurzyński, P., Wójcik, A.: Quantum walk as a generalized measuring device. Phys. Rev. Lett. 110(20), 200404 (2013)
Zhan, X., Qin, H., Bian, Z.H., Li, J., Xue, P.: Perfect state transfer and efficient quantum routing: a discrete-time quantum-walk approach. Phys. Rev. A 90(1), 012331 (2014)
Yalçınkaya, İ., Gedik, Z.: Qubit state transfer via discrete-time quantum walks. J. Phys. A Math. Theor. 48(22), 225302 (2015)
Montero, M.: Quantum and random walks as universal generators of probability distributions. Phys. Rev. A 95(6), 062326 (2017)
Brun, T.A., Carteret, H.A., Ambainis, A.: Quantum walks driven by many coins. Phys. Rev. A 67(5), 052317 (2003)
Tregenna, B., Flanagan, W., Maile, R., Kendon, V.: Controlling discrete quantum walks: coins and initial states. New J. Phys. 5(1), 83 (2003)
Venegas-Andraca, S., Ball, J., Burnett, K., Bose, S.: Quantum walks with entangled coins. New J. Phys. 7(1), 221 (2005)
Liu, C., Petulante, N.: One-dimensional quantum random walks with two entangled coins. Phys. Rev. A 79(3), 032312 (2009)
Liu, C.: Asymptotic distributions of quantum walks on the line with two entangled coins. Quantum Inf. Process. 11(5), 1193 (2012)
Omar, Y., Paunković, N., Sheridan, L., Bose, S.: Quantum walk on a line with two entangled particles. Phys. Rev. A 74(4), 042304 (2006)
Pathak, P., Agarwal, G.: Quantum random walk of two photons in separable and entangled states. Phys. Rev. A 75(3), 032351 (2007)
Berry, S.D., Wang, J.B.: Two-particle quantum walks: entanglement and graph isomorphism testing. Phys. Rev. A 83(4), 042317 (2011)
Štefaňák, M., Barnett, S., Kollár, B., Kiss, T., Jex, I.: Directional correlations in quantum walks with two particles. New J. Phys. 13(3), 033029 (2011)
Rohde, P.P., Schreiber, A., Štefaňák, M., Jex, I., Silberhorn, C.: Multi-walker discrete time quantum walks on arbitrary graphs, their properties and their photonic implementation. New J. Phys. 13(1), 013001 (2011)
Xue, P., Sanders, B.C.: Two quantum walkers sharing coins. Phys. Rev. A 85(2), 022307 (2012)
Rigovacca, L., Di Franco, C.: Two-walker discrete-time quantum walks on the line with percolation. Sci. Rep. 6, 22052 (2016)
Wang, Q., Li, Z.J.: Repelling, binding, and oscillating of two-particle discrete-time quantum walks. Ann. Phys. 373, 1 (2016)
Rohde, P.P., Schreiber, A., Štefaňák, M., Jex, I., Gilchrist, A., Silberhorn, C.: Increasing the dimensionality of quantum walks using multiple walkers. J. Comput. Theor. Nanosci. 10(7), 1644 (2013)
Xu, G., Xiao, K., Li, Z.P., Niu, X.X., Ryan, M.: Controlled secure direct communication protocol via the three-qubit partially entangled set of states. CMC 58(3), 809–827 (2019)
Štefaňák, M., Skoupỳ, S.: Perfect state transfer by means of discrete-time quantum walk on complete bipartite graphs. Quantum Inf. Process. 16(3), 72 (2017)
Innocenti, L., Majury, H., Giordani, T., Spagnolo, N., Sciarrino, F., Paternostro, M., Ferraro, A.: Quantum state engineering using one-dimensional discrete-time quantum walks. Phys. Rev. A 96(6), 062326 (2017)
Yang, Y., Yang, J., Zhou, Y., Shi, W., Chen, X., Li, J., Zuo, H.: Quantum network communication: a discrete-time quantum-walk approach. Sci. China Inf. Sci. 61(4), 042501 (2018)
Li, X.M., Yang, M., Paunković, N., Li, D.C., Cao, Z.L.: Entanglement swapping via three-step quantum walk-like protocol. Phys. Lett. A 381(46), 3875 (2017)
Rajendran, J., Benjamin, C.: Implementing parrondo’s paradox with two-coin quantum walks. Open Sci. 5(2), 171599 (2018)
Wang, Y., Shang, Y., Xue, P.: Generalized teleportation by quantum walks. Quantum Inf. Process. 16(9), 221 (2017)
Bennett, C.H., Brassard, G., Crépeau, 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 (1993)
Yang, C.P., Guo, G.C.: Multiparticle generalization of teleportation. Chin. Phys. Lett. 17(3), 162 (2000)
Lee, J., Min, H., Oh, S.D.: Multipartite entanglement for entanglement teleportation. Phys. Rev. A 66(5), 052318 (2002)
Rigolin, G.: Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement. Phys. Rev. A 71(3), 032303 (2005)
Nandi, K., Mazumdar, C.: Quantum teleportation of a two qubit state using GHZ-like state. Int. J. Theor. Phys. 53(4), 1322 (2014)
Zhao, N., Li, M., Chen, N., Zhu, C.H., Pei, C.X.: Quantum teleportation of eight-qubit state via six-qubit cluster state. Int. J. Theor. Phys. 57(2), 516 (2018)
Hayashi, M.: Prior entanglement between senders enables perfect quantum network coding with modification. Phys. Rev. A 76(4), 040301 (2007)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. U1636106, 61671087, 61170272), Natural Science Foundation of Beijing Municipality (No. 4182006), Technological Special Project of Guizhou Province (Grant No. 20183001), and the Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant Nos. 2018BDKFJJ016, 2018BDKFJJ018).
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Li, HJ., Chen, XB., Wang, YL. et al. A new kind of flexible quantum teleportation of an arbitrary multi-qubit state by multi-walker quantum walks. Quantum Inf Process 18, 266 (2019). https://doi.org/10.1007/s11128-019-2374-7
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DOI: https://doi.org/10.1007/s11128-019-2374-7