logo

SCIENCE CHINA Information Sciences, Volume 61 , Issue 4 : 042501(2018) https://doi.org/10.1007/s11432-017-9190-0

Quantum network communication: a discrete-time quantum-walk approach

More info
  • ReceivedMay 9, 2017
  • AcceptedJul 27, 2017
  • PublishedJan 5, 2018

Abstract


References

[1] Ahlswede R, Ning Cai R, Li S Y R. Network information flow. IEEE Trans Inform Theor, 2000, 46: 1204-1216 CrossRef Google Scholar

[2] Pan Z, Lei J, Zhang Y. Fast Motion Estimation Based on Content Property for Low-Complexity H.265/HEVC Encoder. IEEE Trans Broadcast, 2016, 62: 675-684 CrossRef Google Scholar

[3] Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299: 802-803 CrossRef ADS Google Scholar

[4] Hayashi M, Iwama K, Nishimura H, et al. Quantum network coding. In: Proceedings of Annual Symposium on Theoretical Aspects of Computer Science. Berlin: Springer, 2007. 4393: 610--621. Google Scholar

[5] Hayashi M. Prior entanglement between senders enables perfect quantum network coding with modification. Phys Rev A, 2007, 76: 040301 CrossRef ADS arXiv Google Scholar

[6] Satoh T, Le Gall F, Imai H. Quantum network coding for quantum repeaters. Phys Rev A, 2012, 86: 032331 CrossRef ADS arXiv Google Scholar

[7] Soeda A, Kinjo Y, Turner P S. Quantum computation over the butterfly network. Phys Rev A, 2011, 84: 012333 CrossRef ADS arXiv Google Scholar

[8] Li J, Chen X B, Xu G. Perfect Quantum Network Coding Independent of Classical Network Solutions. IEEE Commun Lett, 2015, 19: 115-118 CrossRef Google Scholar

[9] Li J, Chen X, Sun X. Quantum network coding for multi-unicast problem based on 2D and 3D cluster states. Sci China Inf Sci, 2016, 59: 042301 CrossRef Google Scholar

[10] Mahdian M, Bayramzadeh R. Perfect K-Pair Quantum Network Coding Using Superconducting Qubits. J Supercond Nov Magn, 2015, 28: 345-348 CrossRef Google Scholar

[11] Shang T, Li J, Pei Z. Quantum network coding for general repeater networks. Quantum Inf Process, 2015, 14: 3533-3552 CrossRef ADS Google Scholar

[12] Xu G, Chen X B, Li J. Network coding for quantum cooperative multicast. Quantum Inf Process, 2015, 14: 4297-4322 CrossRef ADS Google Scholar

[13] Shang T, Du G, Liu J. Opportunistic quantum network coding based on quantum teleportation. Quantum Inf Process, 2016, 15: 1743-1763 CrossRef ADS Google Scholar

[14] Kobayashi H, Le Gall F, Nishimura H, et al. Perfect quantum network communication protocol based on classical network coding. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Austin, 2010. 2686--2690. Google Scholar

[15] Kobayashi H, Le Gall F, Nishimura H, et al. Constructing quantum network coding schemes from classical nonlinear protocols. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), St. Petersburg, 2011. 109--113. Google Scholar

[16] Jain A, Franceschetti M, Meyer D A. On quantum network coding. J Math Phys, 2011, 52: 032201-032201 CrossRef ADS Google Scholar

[17] Wang X L, Chen L K, Li W. Experimental Ten-Photon Entanglement. Phys Rev Lett, 2016, 117: 210502 CrossRef PubMed ADS arXiv Google Scholar

[18] Leung D, Oppenheim J, Winter A. Quantum Network Communication-The Butterfly and Beyond. IEEE Trans Inform Theor, 2010, 56: 3478-3490 CrossRef Google Scholar

[19] Aharonov D, Ambainis A, Kempe J, et al. Quantum walks on graphs. In: Proceedings of the 33rd ACM Symposium on Theory of Computing, Hersonissos, 2001. 50--59. Google Scholar

[20] Ambainis A. Quantum Walk Algorithm for Element Distinctness. SIAM J Comput, 2007, 37: 210-239 CrossRef Google Scholar

[21] Magniez F, Santha M, Szegedy M. Quantum Algorithms for the Triangle Problem. SIAM J Comput, 2007, 37: 413-424 CrossRef Google Scholar

[22] Tamascelli D, Zanetti L. A quantum-walk-inspired adiabatic algorithm for solving graph isomorphism problems. J Phys A-Math Theor, 2014, 47: 325302 CrossRef ADS arXiv Google Scholar

[23] Childs A M, Ge Y. Spatial search by continuous-time quantum walks on crystal lattices. Phys Rev A, 2014, 89: 052337 CrossRef ADS arXiv Google Scholar

[24] Babatunde A M, Cresser J, Twamley J. Using a biased quantum random walk as a quantum lumped element router. Phys Rev A, 2014, 90: 012339 CrossRef ADS Google Scholar

[25] Zhan X, Qin H, Bian Z. Perfect state transfer and efficient quantum routing: A discrete-time quantum-walk approach. Phys Rev A, 2014, 90: 012331 CrossRef ADS arXiv Google Scholar

[26] Yalç$\imath~$nkaya .I Gedik Z. Qubit state transfer via discrete-time quantum walks. J Phys A-Math Theor, 2015, 48: 225302. Google Scholar

[27] Travaglione B C, Milburn G J. Implementing the quantum random walk. Phys Rev A, 2002, 65: 032310 CrossRef ADS Google Scholar

[28] Tregenna B, Flanagan W, Maile R. Controlling discrete quantum walks: coins and initial states. New J Phys, 2003, 5: 83-83 CrossRef ADS Google Scholar

[29] Soeda A, Kinjo Y, Turner P S, et al. Quantum computation over the butterfly network. 2011,. arXiv Google Scholar

[30] Rohde P P, Schreiber A, ?tefa?鲸?k M. Increasing the Dimensionality of Quantum Walks Using Multiple Walkers. Jnl Comp Theo Nano, 2013, 10: 1644-1652 CrossRef Google Scholar

[31] Raussendorf R, Browne D E, Briegel H J. Measurement-based quantum computation on cluster states. Phys Rev A, 2003, 68: 022312 CrossRef ADS Google Scholar

  • Table 1   Comparison in terms of resource consumption and fidelity
    Prior entanglement Classical communication Quantum operation Average fidelity Probability
    Ref. [3] Yes Yes Yes $0.5~\le~f~\le~1$ 1
    Refs. [4,~6,~9--14] Yes Yes Yes 1 1
    Refs. [5,~15] Yes Yes Yes 1 $p~\le~1$
    Our scheme No Yes Yes 1 1