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Measurement-based quantum communication

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Abstract

We review and discuss the potential of using measurement-based elements in quantum communication schemes, where certain tasks are realized with the help of entangled resource states that are processed by measurements. We consider long-range quantum communication based on the transmission of encoded quantum states, where encoding, decoding and syndrome readout are implemented using small-scale resource states. We also discuss entanglement-based schemes and consider measurement-based quantum repeaters. An important element in these schemes is entanglement purification, which can also be implemented in a measurement-based way. We analyze the influence of noise and imperfections in these schemes and show that measurement-based implementation allows for very large error thresholds of the order of 10 % noise per qubit and more. We show how to obtain optimal resource states for different tasks and discuss first experimental realizations of measurement-based quantum error correction using trapped ions and photons.

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References

  1. V. Scarani, H. Bechmann-Pasquinucci, N.J. Cerf, M. Dus̆ek, N. Lütkenhaus, M. Peev, Rev. Mod. Phys. 81, 1301 (2009)

    Article  ADS  Google Scholar 

  2. A. Broadbent, J. Fitzsimons, E. Kashefi, in Proceedings of the 50th Annual Symposium on Foundations of Computer Science (IEEE Computer Society, Los Alamitos, CA, 2009), p. 517

  3. Stefanie Barz et al., Science 335, 303 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  4. H.J. Kimble, Nature 453, 1023 (2008)

    Article  ADS  Google Scholar 

  5. E. Knill, R. Laflamme, (1996). arXiv:quanth-ph/9608012

  6. H.J. Briegel, W. Dür, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 81, 5932 (1998)

    Article  ADS  Google Scholar 

  7. C.H. Bennett et al., Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  8. N. Sangouard, C. Simon, H. de Riedmatten, N. Gisin, Rev. Mod. Phys. 83, 33 (2011)

    Article  ADS  Google Scholar 

  9. T. Jennewein, B. Higgins, Quantum space race. Phys World 26(3), 5256 (2013)

    Article  Google Scholar 

  10. P. Shor, Phys. Rev. A 52, 2493 (1995)

    Article  ADS  Google Scholar 

  11. A.M. Steane, Phys. Rev. Lett. 77, 793 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  12. D. Gottesman, Stabilizer codes and quantum error correction. Ph.D. thesis, Caltech (1997), arXiv:quant-ph/9705052

  13. M. Zukowski, A. Zeilinger, M.A. Horne, A.K. Ekert, Phys. Rev. Lett. 71, 4287 (1993)

    Article  ADS  Google Scholar 

  14. C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J.A. Smolin, W.K. Wootters, Phys. Rev. Lett. 76, 722 (1996)

    Article  ADS  Google Scholar 

  15. D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, A. Sanpera, Phys. Rev. Lett. 77, 2818 (1996)

    Article  ADS  Google Scholar 

  16. W. Dür, H.J. Briegel, Rep. Prog. Phys. 70, 1381 (2007)

    Article  ADS  Google Scholar 

  17. R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  18. H.J. Briegel, R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001)

    Article  ADS  Google Scholar 

  19. M. Zwerger, W. Dür, H.J. Briegel, Phys. Rev. A 85, 062326 (2012)

    Article  ADS  Google Scholar 

  20. M. Zwerger, H.J. Briegel, W. Dür, Phys. Rev. Lett. 110, 260503 (2013)

    Article  ADS  Google Scholar 

  21. M. Zwerger, H.J. Briegel, W. Dür, Sci. Rep. 4, 5364 (2014)

    Article  ADS  Google Scholar 

  22. B.P. Lanyon, P. Jurcevic, M. Zwerger, C. Hempel, E.A. Martinez, W. Dür, H.J. Briegel, R. Blatt, C.F. Roos, Phys. Rev. Lett. 111, 210501 (2013)

    Article  ADS  Google Scholar 

  23. S. Barz, R. Vasconcelos, C. Greganti, M. Zwerger, W. Dür, H.J. Briegel, P. Walther, Phys. Rev. A 90, 042302 (2014)

    Article  ADS  Google Scholar 

  24. M. Zwerger, H.J. Briegel, W. Dür, Phys. Rev. A 90, 012314 (2014)

    Article  ADS  Google Scholar 

  25. A. Jamiolkowski, Rep. Math. Phys. 3, 275–278 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  26. M.D. Choi, Linear Algebra Appl. 10, 285–290 (1975)

    Article  Google Scholar 

  27. M.A. Nielsen, I.L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2000)

    MATH  Google Scholar 

  28. E. Knill, Nature 434, 39 (2005)

    Article  ADS  Google Scholar 

  29. R. Raussendorf, J. Harrington, Phys. Rev. Lett. 98, 190504 (2007)

    Article  ADS  Google Scholar 

  30. M. Hein et al., in Proceedings of the International School of Physics “Enrico Fermi” on “Quantum Computers, Algorithms and Chaos” (2005), arXiv:quant-ph/0602096

  31. D. Gottesman, (2009), arXiv:0904.2557

  32. R. Raussendorf, Philos. Trans. R. Soc. A 370, 4541 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  33. H.J. Briegel, D.E. Browne, W. Dür, R. Raussendorf, M. Van den Nest, Nat. Phys. 5, 19 (2009)

    Article  Google Scholar 

  34. C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, Phys. Rev. A 5(4), 3824 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  35. H. Aschauer, Quantum communication in noisy environments, Dissertation, LMU München (2004)

  36. L. Hartmann, B. Kraus, H.J. Briegel, W. Dür, Phys. Rev. A 75, 032310 (2007)

    Article  ADS  Google Scholar 

  37. M.A. Nielsen, Phys. Rev. Lett. 93, 040503 (2004)

    Article  ADS  Google Scholar 

  38. S.D. Barrett, P. Kok, Phys. Rev. A 71, 060310 (2005)

    Article  ADS  Google Scholar 

  39. L.M. Duan, R. Raussendorf, Phys. Rev. Lett. 95, 080503 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  40. D. Gross, K. Kieling, J. Eisert, Phys. Rev. A 74, 042343 (2006)

    Article  ADS  Google Scholar 

  41. K. Kieling, T. Rudolph, J. Eisert, Phys. Rev. Lett. 99, 130501 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  42. D.E. Browne, T. Rudolph, Phys. Rev. Lett. 95, 010501 (2005)

    Article  ADS  Google Scholar 

  43. R. Raussendorf, D.E. Browne, H.J. Briegel, Phys. Rev. A 68, 022312 (2003)

    Article  ADS  Google Scholar 

  44. M. Hein, J. Eisert, H.J. Briegel, Phys. Rev. A 69, 062311 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  45. A. Sørensen, K. Mølmer, Phys. Rev. Lett. 82, 1971 (1999)

    Article  ADS  Google Scholar 

  46. S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. Büchler, P. Zoller, Nat. Phys. 4, 878 (2008)

    Article  Google Scholar 

  47. F. Verstraete, M.M. Wolf, J.I. Cirac, Nat. Phys. 5, 633 (2009)

    Article  Google Scholar 

  48. W. Dür, H. Aschauer, H.J. Briegel, Phys. Rev. Lett. 91, 107903 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  49. S. Glancy, E. Knill, H.M. Vasconcelos, Phys. Rev. A 74, 032319 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  50. C. Kruszynska, A. Miyake, H.J. Briegel, W. Dür, Phys. Rev. A 74, 052316 (2006)

    Article  ADS  Google Scholar 

  51. J. Wallnöfer, W. Dür, in preparation

  52. M. Hein, W. Dür, H.J. Briegel, Phys. Rev. A 71, 032350 (2005)

    Article  ADS  Google Scholar 

  53. F. Kesting, F. Fröwis, W. Dür, Phys. Rev. A 88, 042305 (2013)

    Article  ADS  Google Scholar 

  54. J. Fern, K.B. Whaley, Phys. Rev. A 78, 062335 (2008)

    Article  ADS  Google Scholar 

  55. C. H. Bennett, G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, 175, 8 (1984)

  56. A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  57. W. Dür, M. Skotiniotis, F. Fröwis, B. Kraus, Phys. Rev. Lett. 112, 080801 (2014)

    Article  Google Scholar 

  58. G. Arrad, Y. Vinkler, D. Aharonov, A. Retzker, Phys. Rev. Lett. 112, 150801 (2014)

    Article  ADS  Google Scholar 

  59. E.M. Kessler, I. Lovchinsky, A.O. Sushkov, M.D. Lukin, Phys. Rev. Lett. 112, 150802 (2014)

    Article  ADS  Google Scholar 

  60. S. Muralidharan, J. Kim, N. Lütkenhaus, M.D. Lukin, L. Jiang, Phys. Rev. Lett. 112, 250501 (2014)

    Article  ADS  Google Scholar 

  61. S. Bravyi, A. Kitaev, Phys. Rev. A 71, 022316 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  62. P. Walther, K.J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, A. Zeilinger, Nature 434, 169 (2005)

    Article  ADS  Google Scholar 

  63. R. Prevedel, P. Walther, F. Tiefenbacher, P. Böhi, R. Kaltenbaek, T. Jennewein, A. Zeilinger, Nature 445, 65 (2007)

    Article  ADS  Google Scholar 

  64. W.-B. Gao, A.M. Goebel, C.-Y. Lu, H.-N. Dai, C. Wagenknecht, Q. Zhang, B. Zhao, C.-Z. Peng, Z.-B. Chen, Y.-A. Chen, J.-W. Pan, PNAS 107(49), 20869–20874 (2010)

    Article  ADS  Google Scholar 

  65. L. Jiang, J.M. Taylor, K. Nemoto, W.J. Munro, R. Van Meter, M.D. Lukin, Phys. Rev. A 79, 032325 (2009)

    Article  ADS  Google Scholar 

  66. N.K. Bernardes, P. van Loock, Phys. Rev. A 86, 052301 (2012)

    Article  ADS  Google Scholar 

  67. F. Ewert, M. Bergmann, P. van Loock, (2015), arXiv:1503.06777

  68. K. Azuma, K. Tamaki, H.-K. Lo, Nat. Commun. 6, 6787 (2015)

    Article  ADS  Google Scholar 

  69. U.L. Andersen, J.S. Neergaard-Nielsen, P. van Loock, A. Furusawa, Nat. Phys. 11, 713–719 (2015)

    Article  Google Scholar 

  70. M. Zwerger et al., in preparation

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Acknowledgments

This work was supported by the Austrian Science Fund (FWF): P24273-N16, P28000-N27, SFB F40-FoQus F4012-N16.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 21a, 6020, Innsbruck, Austria

    M. Zwerger, H. J. Briegel & W. Dür

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  1. M. Zwerger
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  2. H. J. Briegel
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  3. W. Dür
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Correspondence to W. Dür.

Additional information

This paper is part of the topical collection “Quantum Repeaters: From Components to Strategies” guest edited by Manfred Bayer, Christoph Becher and Peter van Loock.

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Zwerger, M., Briegel, H.J. & Dür, W. Measurement-based quantum communication. Appl. Phys. B 122, 50 (2016). https://doi.org/10.1007/s00340-015-6285-8

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