Skip to main content
SpringerLink
Log in

Generating multi-mode entangled coherent W and GHZ states via optical system based fusion mechanism

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Fusion technology has been demonstrated to be a good method for generating a large-scale entangled coherent W or GHZ state from two small ones in QED system. It is of importance to study how to fuse small-scale entangled coherent W or GHZ states via optical system. In this paper, we present a scheme for generating larger entangled coherent W or GHZ state in an optical system by virtue of fusion technology. The key fusion mechanism is realized by photon detectors and a Mach–Zehnder interferometer with its two arms immersed in Kerr media, by which an n-mode entangled coherent W state and an m-mode entangled coherent W state can be probabilistically fused into an (\(n+m-2\))-mode entangled coherent W state. This fusion scheme applies to entangled coherent GHZ state too but with a unit probability of success. Feasibility analysis indicates that our fusion scheme may be realized with current experimental technology. Large-scale entangled coherent W and GHZ states may find new applications in quantum communication.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  1. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  Google Scholar 

  2. Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 022312 (2003)

    Article  ADS  Google Scholar 

  3. Özdemir, S.K., Shimamura, J., Imoto, N.: A necessary and sufficient condition to play games in quantum mechanical settings. New J. Phys. 9(2), 43 (2007)

    Article  Google Scholar 

  4. Shimamura, J., Özdemir, Ş.K., Morikoshi, F., Imoto, N.: Entangled states that cannot reproduce original classical games in their quantum version. Phys. Lett. A 328(1), 20–25 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Shimamura, J., Özdemir, Ş.K., Morikoshi, F., Imoto, N.: Quantum and classical correlations between players in game theory. Int. J. Quantum Inf. 2(01), 79–89 (2004)

    Article  MATH  Google Scholar 

  6. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. 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, 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575 (1997)

    Article  ADS  Google Scholar 

  10. Özdemir, Ş.K., Bartkiewicz, K., Liu, Y.X., Miranowicz, A.: Teleportation of qubit states through dissipative channels: conditions for surpassing the no-cloning limit. Phys. Rev. A 76(4), 042325 (2007)

    Article  ADS  Google Scholar 

  11. Dăg, C.B., Niedenzu, W., Müstecaplıŏglu, O.E., Kurizki, G.: Multiatom quantum coherences in micromasers as fuel for thermal and nonthermal machines. Entropy 18, 244 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  12. Greenberger, D.M., et al.: In: Kafatos, M. (ed.) Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, p. 69. Kluwer, Dordrecht (1989)

    Google Scholar 

  13. Dür, W.: Multipartite entanglement that is robust against disposal of particles. Phys. Rev. A 63, 020303(R) (2001)

    Article  ADS  Google Scholar 

  14. Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910 (2001)

    Article  ADS  Google Scholar 

  15. Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev. 93(1), 99 (1954)

    Article  ADS  MATH  Google Scholar 

  16. Zhao, Z., Chen, Y.A., Zhang, A.N., Yang, T., Briegel, H.J., Pan, J.W.: Experimental demonstration of five-photon entanglement and open-destination teleportation. Nature 430, 54 (2004)

    Article  ADS  Google Scholar 

  17. Kempe, J.: Multiparticle entanglement and its applications to cryptography. Phys. Rev. A 60, 910 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  18. D’Hondt, E., Panangaden, P.: The computational power of the W and GHZ states. Quantum Inf. Comput. 6, 173 (2006)

    MathSciNet  MATH  Google Scholar 

  19. Kiesel, N., Schmid, C., Tóth, G., Solano, E., Weinfurter, H.: Experimental observation of four-photon entangled Dicke state with high fidelity. Phys. Rev. Lett. 98(6), 063604 (2007)

    Article  ADS  Google Scholar 

  20. Wieczorek, W., Krischek, R., Kiesel, N., Michelberger, P., Tóth, G., Weinfurter, H.: Experimental entanglement of a six-photon symmetric Dicke state. Phys. Rev. Lett. 103(2), 020504 (2009)

    Article  ADS  Google Scholar 

  21. Tashima, T., Tame, M.S., Özdemir, Ş.K., Nori, F., Koashi, M., Weinfurter, H.: Photonic multipartite entanglement conversion using nonlocal operations. Phys. Rev. A 94(5), 052309 (2016)

    Article  ADS  Google Scholar 

  22. Cui, W.X., Hu, S., Wang, H.F., Zhu, A.D., Zhang, S.: Deterministic conversion of a four-photon GHZ state to a W state via homodyne measurement. Opt. Express 24(14), 15319–15327 (2016)

    Article  ADS  Google Scholar 

  23. Tashima, T., Wakatsuki, T., Özdemir, Ş.K., Yamamoto, T., Koashi, M., Imoto, N.: Local transformation of two Einstein–Podolsky–Rosen photon pairs into a three-photon W state. Phys. Rev. Lett. 102(13), 130502 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Kobayashi, T., Ikuta, R., Özdemir, Ş.K., Tame, M., Yamamoto, T., Koashi, M., Imoto, N.: Universal gates for transforming multipartite entangled Dicke states. New J. Phys. 16(2), 023005 (2014)

    Article  ADS  Google Scholar 

  25. Resch, K.J., Walther, P., Zeilinger, A.: Full characterization of a three-photon Greenberger–Horne–Zeilinger state using quantum state tomography. Phys. Rev. Lett. 94(7), 070402 (2005)

    Article  ADS  Google Scholar 

  26. Mikami, H., Li, Y., Fukuoka, K., Kobayashi, T.: New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography. Phys. Rev. Lett. 95(15), 150404 (2005)

    Article  ADS  Google Scholar 

  27. Guo, G.P., Li, C.F., Li, J., Guo, G.C.: Scheme for the preparation of multiparticle entanglement in cavity QED. Phys. Rev. A 65, 042102 (2002)

    Article  ADS  Google Scholar 

  28. Reiserer, A., Rempe, G.: Cavity-based quantum networks with single atoms and optical photons. Rev. Mod. Phys. 87(4), 1379 (2015)

    Article  ADS  Google Scholar 

  29. Eibl, M., Kiesel, N., Bourennane, M., Kurtsiefer, C., Weinfurter, H.: Experimental realization of a three-qubit entangled W state. Phys. Rev. Lett. 92, 077901 (2004)

    Article  ADS  Google Scholar 

  30. Shi, J., et al.: Heralded generation of multipartite entanglement for one photon by using a single two-dimensional nonlinear photonic crystal. Opt. Express 21(7), 7875 (2013)

    Article  ADS  Google Scholar 

  31. Yesilyurt, C., Bugu, S., Diker, F., Altintasd, A.A., Ozaydina, F.: An optical setup for deterministic creation of four partite W state. Acta Phys. Pol. A 127(4), 1230–1232 (2015)

    Article  Google Scholar 

  32. Moreno, M.G.M., Cunha, M.M., Parisio, F.: Remote preparation of W states from imperfect bipartite sources. Quantum Inf. Process. 15(9), 3869–3879 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Duan, L.M., Monroe, C.: Colloquium: Quantum networks with trapped ions. Rev. Mod. Phys. 82, 1209 (2010)

    Article  ADS  Google Scholar 

  34. Roos, C.F., et al.: Control and measurement of three-qubit entangled states. Science 304(5676), 1478 (2004)

    Article  ADS  Google Scholar 

  35. Häffner, H., et al.: Scalable multiparticle entanglement of trapped ions. Nature 438, 643 (2005)

    Article  ADS  Google Scholar 

  36. Özdemir, Ş.K., Matsunaga, E., Tashima, T., Yamamoto, T., Koashi, M., Imoto, N.: An optical fusion gate for W-states. New J. Phys. 13, 103003 (2011)

    Article  Google Scholar 

  37. Ozaydin, F., Bugu, S., Yesilyurt, C., Altintas, A.A., Tame, M., Özdemir, Ş.K.: Fusing multiple W states simultaneously with a Fredkin gate. Phys. Rev. A 89, 042311 (2014)

    Article  ADS  Google Scholar 

  38. Yesilyurt, C., Bugu, S., Ozaydin, F.: An optical gate for simultaneous fusion of four photonic W or Bell states. Quantum Inf. Process. 12, 2965 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Bugu, S., Yesilyurt, C., Ozaydin, F.: Enhancing the W-state quantum-network-fusion process with a single Fredkin gate. Phys. Rev. A 87, 032331 (2013)

    Article  ADS  Google Scholar 

  40. Zang, X.P., Yang, M., Wang, X.C., Song, W., Cao, Z.L.: Fusion of W states in cavity QED system. Can. J. Phys. 93, 556 (2015)

    Article  ADS  Google Scholar 

  41. Zang, X.P., Yang, M., Ozaydin, F., Song, W., Cao, Z.L.: Generating multi-atom entangled W states via light-matter interface based fusion mechanism. Sci. Rep. 5, 16245 (2015)

    Article  ADS  Google Scholar 

  42. Zang, X.P., Yang, M., Song, W., Cao, Z.L.: Fusion of entangled coherent W and GHZ states in cavity QED. Opt. Commun. 370, 168 (2016)

    Article  ADS  Google Scholar 

  43. Dikera, F., Ozaydinb, F., Arika, M.: Enhancing the W state fusion process with a to oli gate and a CNOT gate via one-way quantum computation and linear optics. Acta Phys. Pol. A 127(4), 1189–1190 (2015)

    Article  Google Scholar 

  44. Li, N., Yang, J., Ye, L.: Realizing an efficient fusion gate for W states with cross-Kerr nonlinearities and QD-cavity coupled system. Quantum Inf. Process. 14(6), 1933–1946 (2015)

    Article  ADS  MATH  Google Scholar 

  45. Li, K., Kong, F.Z., Yang, M., Yang, Q., Cao, Z.L.: Qubit-loss-free fusion of W states. Phys. Rev. A 94(6), 062315 (2016)

    Article  ADS  Google Scholar 

  46. Tashima, T., Özdemir, Ş.K., Yamamoto, T., Koashi, M., Imoto, N.: Elementary optical gate for expanding an entanglement web. Phys. Rev. A 77, 030302 (2008)

    Article  ADS  MATH  Google Scholar 

  47. Tashima, T., Özdemir, Ş.K., Yamamoto, T., Koashi, M., Imoto, N.: Local expansion of photonic W state using a polarization-dependent beamsplitter. New J. Phys. 11, 023024 (2009)

    Article  ADS  Google Scholar 

  48. Zang, X.P., Yang, M., Wu, W.F., Fang, S.D., Cao, Z.L.: Local expansion of atomic W state in cavity quantum electrodynamics. Indian J. Phys. 88, 1141 (2014)

    Article  ADS  Google Scholar 

  49. Zang, X.P., Yang, M., Ozaydin, F., Song, W., Cao, Z.L.: Deterministic generation of large scale atomic W states. Opt. Express 24, 12293 (2016)

    Article  ADS  Google Scholar 

  50. Yesilyurt, C., Bugu, S., Ozaydin, F., Altintas, A.A., Tame, M., Yang, L., Özdemir, Ş.K.: Deterministic local expansion of W states. J. Opt. Soc. Am. B 33, 2313 (2016)

    Article  ADS  Google Scholar 

  51. Tashima, T., Kitano, T., Özdemir, Ş.K., Yamamoto, T., Koashi, M., Imoto, N.: Demonstration of local expansion toward large-scale entangled webs. Phys. Rev. lett. 105(21), 210503 (2010)

    Article  ADS  Google Scholar 

  52. Fuchs, C.A.: Nonorthogonal quantum states maximize classical information capacity. Phys. Rev. Lett. 79, 1162 (1997)

    Article  ADS  Google Scholar 

  53. Glauber, R.J.: Coherent and incoherent states of radiation field. Phys. Rev. 131, 2766–2788 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  54. Zhang, W.M., Feng, D.H., Gilmore, R.: Coherent states: theory and some applications. Rev. Mod. Phys. 62, 867–927 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  55. Sanders, B.C., Rice, D.A.: Nonclassical fields and the nonlinear interferometer. Phys. Rev. A 61, 013805 (1999)

    Article  ADS  Google Scholar 

  56. Chai, C.L.: Two-mode nonclassical state via superpositions of two-mode coherent states. Phys. Rev. A 46, 7187 (1992)

    Article  ADS  Google Scholar 

  57. An, N.B.: Optimal processing of quantum information via W-type entangled coherent states. Phys. Rev. A 69, 022315 (2004)

    Article  ADS  Google Scholar 

  58. Van Enk, S.J., Hirota, O.: Entangled coherent states: teleportation and decoherence. Phys. Rev. A 64, 022313 (2001)

    Article  ADS  Google Scholar 

  59. Clausen, J., Knöl, L., Welsch, D.G.: Lossy purification and detection of entangled coherent states. Phys. Rev. A 66, 062303 (2002)

    Article  ADS  Google Scholar 

  60. Jeong, H., Kim, M.S.: Efficient quantum computation using coherent states. Phys. Rev. A 65, 042305 (2002)

    Article  ADS  Google Scholar 

  61. Ralph, T.C., Gilchrist, A., Milburn, G.J., Munro, W.J., Glancy, S.: Quantum computation with optical coherent states. Phys. Rev. A 68, 042319 (2003)

    Article  ADS  Google Scholar 

  62. Yuan, C.H., Ou, Y.C., Zhang, Z.M.: A scheme for preparation of W-type entangled coherent state of three-cavity fields. Chin. Phys. Lett. 23, 1695 (2006)

    Article  ADS  Google Scholar 

  63. Jeong, H., An, N.B.: Greenberger–Horne–Zeilinger-type and W-type entangled coherent states: generation and Bell-type inequality tests without photon counting. Phys. Rev. A 74, 022104 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  64. Gerry, C.C., Grobe, R.: Nonlocal entanglement of coherent states, complementarity, and quantum erasure. Phys. Rev. A 75, 034303 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  65. Wildfeuer, C.F., Pearlman, A.J., Chen, J., Fan, J., Migdall, A., Dowling, J.P.: Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector. Phys. Rev. A 80(4), 043822 (2009)

    Article  ADS  Google Scholar 

  66. Miller, A.J., Nam, S.W., Martinis, J.M., Sergienko, A.V.: Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination. Appl. Phys. Lett. 83(4), 791–793 (2003)

    Article  ADS  Google Scholar 

  67. Lita, A.E., Miller, A.J., Nam, S.W.: Counting near-infrared single-photons with 95% efficiency. Opt. Express 16(5), 3032–3040 (2008)

    Article  ADS  Google Scholar 

  68. Marsili, F., Verma, V.B., Stern, J.A., Harrington, S., Lita, A.E., Gerrits, T., Vayshenker, I., Baek, B., Shaw, M.D., Mirin, R.P., Nam, S.W.: Detecting single infrared photons with \(93\%\) system efficiency. Nat. Photon. 7, 210–214 (2013)

    Article  ADS  Google Scholar 

  69. Kok, P., Lee, H., Dowling, J.P.: Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements. Phys. Rev. A 66, 063814 (2002)

    Article  ADS  Google Scholar 

  70. Harris, S.E., Hau, L.V.: Nonlinear optics at low light levels. Phys. Rev. Lett. 82, 4611–4614 (1999)

    Article  ADS  Google Scholar 

  71. Lukin, M.D., Imamoglu, A.: Nonlinear optics and quantum entanglement of ultraslow single photons. Phys. Rev. Lett. 84, 1419–1422 (2000)

    Article  ADS  Google Scholar 

  72. Lukin, M.D., Imamoglu, A.: Controlling photons using electromagnetically induced transparency. Nature (London) 413, 273–276 (2001)

    Article  ADS  Google Scholar 

  73. Munro, W.J., Nemoto, K., Beausoleil, R.G., Spiller, T.P.: High-efficiency quantum-nondemolition singlephoton-number-resolving detector. Phys. Rev. A 71, 033819 (2005)

    Article  ADS  Google Scholar 

  74. Xiao, Y.F., Özdemir, Ş.K., Gaddam, V., Dong, C.H., Imoto, N., Yang, L.: Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity. Opt. Express 16(26), 21462–21475 (2008)

    Article  ADS  Google Scholar 

  75. He, B., Scherer, A.: Continuous-mode effects and photonphoton phase gate performance. Phys. Rev. A 85, 033814 (2012)

    Article  ADS  Google Scholar 

  76. Fan, B., Kockum, A.F., Combes, J., Johansson, G., Hoi, I.C., Wilson, C.M., Delsing, P., Milburn, G.J., Stace, T.M.: Breakdown of the cross-Kerr scheme for photon counting. Phys. Rev. Lett. 110, 053601 (2013)

    Article  ADS  Google Scholar 

  77. Munro, W.J., Nemoto, K., Spiller, T.P.: Weak nonlinearities: a new route to optical quantum computation. New J. Phys. 7(1), 137 (2005)

    Article  ADS  Google Scholar 

  78. Lin, Q., Li, J.: Quantum control gates with weak cross-Kerr nonlinearity. Phys. Rev. A 79(2), 022301 (2009)

    Article  ADS  Google Scholar 

  79. Gerry, C.C., Bui, T.: Quantum non-demolition measurement of photon number using weak nonlinearities. Phys. Lett. A 372, 7101 (2008)

    Article  ADS  MATH  Google Scholar 

  80. He, B., Nadeem, M., Bergou, J.: Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity. Phys. Rev. A 79, 035802 (2009)

    Article  ADS  Google Scholar 

  81. Lin, Q., He, B., Bergou, J.A., Ren, Y.: Processing multiphoton states through operation on a single photon: methods and applications. Phys. Rev. A 80, 042311 (2009)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation of China (NSFC) under Grants Nos. 11274010 and 11374085, the Key Program of the Outstanding Young Talent of Anhui Province under Grant Nos. gxyqZD2016206, gxyqZD2016368, gxyqZD2016369 and gxyqZD2016370, the Key Program of the Education Department of Anhui Province under Grant No. KJ2016A511.

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, University of Science and Technology of China, Heifei, 230026, China

    Xue-Ping Zang, Wei-Feng Wu & Hong-Yi Fan

  2. School of Mechatronic Engineering, Chizhou University, Chizhou, 247000, China

    Xue-Ping Zang & Wei-Feng Wu

  3. School of Physics and Material Science, Anhui University, Hefei, 230601, China

    Ming Yang

Authors
  1. Xue-Ping Zang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ming Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei-Feng Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hong-Yi Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ming Yang .

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zang, XP., Yang , M., Wu, WF. et al. Generating multi-mode entangled coherent W and GHZ states via optical system based fusion mechanism. Quantum Inf Process 16, 135 (2017). https://doi.org/10.1007/s11128-017-1591-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-017-1591-1

Keywords

Search

Navigation