Skip to main content
SpringerLink
Log in

Analysis of optical parity gates of generating Bell state for quantum information and secure quantum communication via weak cross-Kerr nonlinearity under decoherence effect

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We demonstrate the advantages of an optical parity gate using weak cross-Kerr nonlinearities (XKNLs), quantum bus (qubus) beams, and photon number resolving (PNR) measurement through our analysis, utilizing a master equation under the decoherence effect (occurred the dephasing and photon loss). To generate Bell states, parity gates based on quantum non-demolition measurement using XKNL are extensively employed in quantum information processing. When designing a parity gate via XKNL, the parity gate can be diversely constructed according to the measurement strategies. In practice, the interactions of XKNLs in optical fiber are inevitable under the decoherence effect. Thus, by our analysis of the decoherence effect, we show that the designed parity gate employing homodyne measurement would not be expected to provide reliable quantum operation. Furthermore, compared with a parity gate using a displacement operator and PNR measurement, we conclude there is experimental benefit from implementation of a parity gate via qubus beams and PNR measurement under the decoherence effect.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings, 35th Annual Symposium on Foundations of Computer Science, vol. 124 (1994)

  2. Loock, P.V., Munro, W.J., Nemoto, K., Spiller, T.P., Ladd, T.D., Braunstein, S.L., Milburn, G.J.: Hybrid quantum computation in quantum optics. Phys. Rev. A 78, 022303 (2008)

    Article  ADS  Google Scholar 

  3. Lin, Q., He, B.: Addendum to single-photon logic gates using minimum resources. Phys. Rev. A 82, 064303 (2010)

    Article  ADS  Google Scholar 

  4. Wang, H.F., Zhang, S., Zhu, A.D., Yeon, K.H.: Fast and effective implementation of discrete quantum Fourier transform via virtual-photon-induced process in separate cavities. J. Opt. Soc. Am. B 29, 1078 (2012)

    Article  ADS  Google Scholar 

  5. Heo, J., Kang, M.S., Hong, C.H., Yang, H., Choi, S.G.: Discrete quantum Fourier transform using weak cross-Kerr nonlinearity and displacement operator and photon-number-resolving measurement under the decoherence effect. Quantum Inf. Process. 15, 4955 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  7. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., 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 

  8. Heo, J., Hong, C.H., Lee, D.H., Yang, H.J.: Bidirectional transfer of quantum information for unknown photons via cross-Kerr nonlinearity and photon-number-resolving measurement. Chin. Phys. B 25, 020306 (2016)

    Article  Google Scholar 

  9. Liu, H., Ma, H., Wei, K., Yang, X., Qu, W., Dou, T., Chen, Y., Li, R., Zhu, W.: Multi-group dynamic quantum secret sharing with single photons. Phys. Lett. A 380, 2349 (2016)

    Article  ADS  Google Scholar 

  10. Heo, J., Kang, M.S., Hong, C.H., Choi, S.G., Hong, J.P.: Scheme for secure swapping two unknown states of a photonic qubit and an electron-spin qubit using simultaneous quantum transmission and teleportation via quantum dots inside single-sided optical cavities. Phys. Lett. A (2017). doi:10.1016/j.physleta.2017.01.052

  11. Ren, B.C., Du, F.F., Deng, F.G.: Two-step hyperentanglement purification with the quantum-state-joining method. Phys. Rev. A 90, 052309 (2014)

    Article  ADS  Google Scholar 

  12. Tan, X., Zhang, X.: Controlled quantum secure direct communication by entanglement distillation or generalized measurement. Quantum Inf. Process. 15, 2137 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Huber, T., Ostermann, L., Prilmüller, M., Solomon, G.S., Ritsch, H., Weihs, G., Predojević, A.: Coherence and degree of time-bin entanglement from quantum dots. Phys. Rev. B 93, 201301(R) (2016)

    Article  ADS  Google Scholar 

  14. Heo, J., Kang, M.S., Hong, C.H., Yang, H., Choi, S.G.: Schemes generating entangled states and entanglement swapping between photons and three-level atoms inside optical cavities for quantum communication. Quantum Inf. Process. 16, 24 (2017)

    Article  ADS  Google Scholar 

  15. Gao, C.Y., Wang, G.Y., Zhang, H., Deng, F.G.: Multi-photon self-error-correction hyperentanglement distribution over arbitrary collective-noise channels. Quantum Inf. Process. 16, 11 (2017)

    Article  ADS  Google Scholar 

  16. Heo, J., Kang, M.S., Hong, C.H., Choi, S.G., Hong, J.P.: Constructions of secure entanglement channels assisted by quantum dots inside single-sided optical cavities. Opt. Commun. (2017). doi:10.1016/j.optcom.2017.01.056

  17. Nemoto, K., Munro, W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004)

    Article  ADS  Google Scholar 

  18. Barrett, S.D., Kok, P., Nemoto, K., Beausoleil, R.G., Munro, W.J., Spiller, T.P.: Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities. Phys. Rev. A 71, 060302 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Guo, Q., Bai, J., Cheng, L.Y., Shao, X.Q., Wang, H.F., Zhang, S.: Simplified optical quantum-information processing via weak cross-Kerr nonlinearities. Phys. Rev. A 83, 054303 (2011)

    Article  ADS  Google Scholar 

  21. Zhao, R.T., Guo, Q., Cheng, L.Y., Sun, L.L., Wang, H.F., Zhang, S.: Two-qubit and three-qubit controlled gates with cross-Kerr nonlinearity. Chin. Phys. B 22, 030313 (2013)

    Article  ADS  Google Scholar 

  22. Heo, J., Hong, C.H., Lim, J.I., Yang, H.J.: Bidirectional quantum teleportation of unknown photons using path-polarization intra-particle hybrid entanglement and controlled-unitary gates via cross-Kerr nonlinearity. Chin. Phys. B 24, 050304 (2015)

    Article  ADS  Google Scholar 

  23. Jin, G.S., Lin, Y., Wu, B.: Generating multiphoton Greenberger–Horne–Zeilinger states with weak cross-Kerr nonlinearity. Phys. Rev. A 75, 054302 (2007)

    Article  ADS  Google Scholar 

  24. Zheng, C.H., Zhao, J., Shi, P., Li, W.D., Gu, Y.J.: Generation of three-photon polarization-entangled GHZ state via linear optics and weak cross-Kerr nonlinearity. Opt. Commun. 316, 26 (2014)

    Article  ADS  Google Scholar 

  25. Heo, J., Hong, C.H., Lim, J.I., Yang, H.J.: Simultaneous quantum transmission and teleportation of unknown photons using intra- and inter-particle entanglement controlled-not gates via cross-kerr nonlinearity and P-homodyne measurements. Int. J. Theor. Phys. 54, 2261 (2015)

    Article  MATH  Google Scholar 

  26. Louis, S.G.R., Nemoto, K., Munro, W.J., Spiller, T.P.: The efficiencies of generating cluster states with weak nonlinearities. New J. Phys. 9, 193 (2007)

    Article  ADS  Google Scholar 

  27. He, B., Ren, Y., Bergou, J.A.: Creation of high-quality long-distance entanglement with flexible resources. Phys. Rev. A 79, 052323 (2009)

    Article  ADS  Google Scholar 

  28. Lin, Q., He, B.: Single-photon logic gates using minimal resources. Phys. Rev. A 80, 042310 (2009)

    Article  ADS  Google Scholar 

  29. 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 

  30. Lin, Q., He, B.: Weaving independently generated photons into an arbitrary graph state. Phys. Rev. A 84, 062312 (2011)

    Article  ADS  Google Scholar 

  31. Zhu, M.Z., Ye, L.: Efficient distributed controlled Z gate without ancilla single-photons via cross-phase modulation. J. Opt. Soc. Am. B 31, 405 (2014)

    Article  ADS  Google Scholar 

  32. Zhu, M.Z., Ye, L.: Efficient entanglement purification for Greenberger–Horne–Zeilinger states via the distributed parity-check detector. Opt. Commun. 334, 51 (2015)

    Article  ADS  Google Scholar 

  33. Lin, Q., He, B.: Highly efficient processing of multi-photon states. Sci. Rep. 5, 12792 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. Jeong, H.: Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation. Phys. Rev. A 72, 034305 (2005)

    Article  ADS  Google Scholar 

  36. Jeong, H.: Quantum computation using weak nonlinearities: robustness against decoherence. Phys. Rev. A 73, 052320 (2006)

    Article  ADS  Google Scholar 

  37. Barrett, S.D., Milburn, G.J.: Quantum-information processing via a lossy bus. Phys. Rev. A 74, 060302 (2006)

    Article  ADS  Google Scholar 

  38. Wittmann, C., Andersen, U.L., Takeoka, M., Sych, D., Leuchs, G.: Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector. Phys. Rev. A 81, 062338 (2010)

    Article  ADS  Google Scholar 

  39. Knill, E., Laflamme, R., Milburn, G.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)

    Article  ADS  MATH  Google Scholar 

  40. Wang, X.W., Zhang, D.Y., Tang, S.Q., Xie, L.J., Wang, Z.Y., Kuang, L.M.: Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity. Phys. Rev. A 85, 052326 (2012)

    Article  ADS  Google Scholar 

  41. Wang, X.W., Tang, S.Q., Xie, L.J., Zhang, D.Y.: Nondestructive two-photon parity detector with near unity efficiency. Opt. Commun. 296, 153 (2013)

    Article  ADS  Google Scholar 

  42. Ding, D., Yan, F.L., Gao, T.: Entangler and analyzer for multiphoton Greenberger–Horne–Zeilinger states using weak nonlinearities. Sci. China Phys. Mech. Astron. 57, 2098 (2014)

    Article  ADS  Google Scholar 

  43. Liu, Q., Wang, G.Y., Ai, Q., Zhang, M., Deng, F.G.: Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity. Sci. Rep. 6, 22016 (2016)

    Article  ADS  Google Scholar 

  44. Dong, L., Wang, J.X., Li, Q.Y., Dong, H.K., Xiu, X.M., Gao, Y.J.: Teleportation of a general two-photon state employing a polarization-entangled \(\chi \) state with nondemolition parity analyses. Quantum Inf. Process. 15, 2955 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Phoenix, S.J.D.: Wave-packet evolution in the damped oscillator. Phys. Rev. A 41, 5132 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  46. Kok, K., Braunstein, S.L.: Postselected versus nonpostselected quantum teleportation using parametric down-conversion. Phys. Rev. A 61, 042304 (2000)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  48. Lukin, M.D., Imamoğlu, A.: Controlling photons using electromagnetically induced transparency. Nature 413, 273 (2001)

    Article  ADS  Google Scholar 

  49. Kok, P., Munro, W.J., Nemoto, K., Ralph, T.C., Dowling, J.P., Milburn, G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135 (2007)

    Article  ADS  Google Scholar 

  50. Gea-Banacloche, J.: Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets. Phys. Rev. A 81, 043823 (2010)

    Article  ADS  Google Scholar 

  51. He, B., Lin, Q., Simon, C.: Cross-Kerr nonlinearity between continuous-mode coherent states and single photons. Phys. Rev. A 83, 053826 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  53. Kok, P.: Effects of self-phase-modulation on weak nonlinear optical quantum gates. Phys. Rev. A 77, 013808 (2008)

    Article  ADS  Google Scholar 

  54. Sanders, B.C., Milburn, G.J.: Complementarity in a quantum nondemolition measurement. Phys. Rev. A 39, 694 (1989)

    Article  ADS  Google Scholar 

  55. Sanders, B.C., Milburn, G.J.: Quantum limits to all-optical phase shifts in a Kerr nonlinear medium. Phys. Rev. A 45, 1919 (1992)

    Article  ADS  Google Scholar 

  56. Kanamori, H., Yokota, H., Tanaka, G., Watanabe, M., Ishiguro, Y., Yoshida, I., Kakii, T., Itoh, S., Asano, Y., Tanaka, S.: Transmission characteristics and reliability of pure-silica-core single-mode fibers. J. Lightwave Technol. 4, 1144 (1986)

    Article  ADS  Google Scholar 

  57. Nagayama, K., Matsui, M., Kakui, M., Saitoh, T., Kawasaki, K., Takamizawa, H., Ooga, Y., Tsuchiya, I., Chigusa, Y.: Ultra low loss (0.1484 dB/km) pure silica core fiber. SEI Tech. Rev. 57, 3 (2004)

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2015R1A2A2A03004152).

Author information

Authors and Affiliations

  1. College of Electrical and Computer Engineering, Chungbuk National University, Chungdae-ro 1, Seowon-Gu, Cheongju, Republic of Korea

    Jino Heo, Jong-Phil Hong & Seong-Gon Choi

  2. National Security Research Institute, P.O. Box 1, Yuseong, Daejeon, 34188, Republic of Korea

    Chang-Ho Hong

  3. Department of Physics, Korea University, Sejong, 339-700, Republic of Korea

    Hyung-Jin Yang

Authors
  1. Jino Heo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chang-Ho Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hyung-Jin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jong-Phil Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Seong-Gon Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seong-Gon Choi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Heo, J., Hong, CH., Yang, HJ. et al. Analysis of optical parity gates of generating Bell state for quantum information and secure quantum communication via weak cross-Kerr nonlinearity under decoherence effect. Quantum Inf Process 16, 110 (2017). https://doi.org/10.1007/s11128-017-1560-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-017-1560-8

Keywords

Search

Navigation