Skip to main content
Log in

Single-photon controlled multi-photon polarization unitary gate based on weak cross-Kerr nonlinearities

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

With the help of weak cross-Kerr nonlinearities, we propose a single-photon controlled multi-photon polarization unitary gate, which can fulfill the task of n single-photon controlled one-photon polarization unitary gates, but only by adopting a nondestructive measurement and an auxiliary coherent state. Moreover, simple linear optical elements and mature existing techniques containing Homodyne measurement and classical feed-forward are applied. So this scheme provides an efficient and feasible approach for optimally fulfilling single-photon controlled multi-photon unitary gate.

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

Access this article

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

Similar content being viewed by others

References

  1. Barenco, A., Deutsch, D., Ekert, A., Jozsa, R.: Conditional quantum dynamics and logic gates. Phys. Rev. Lett. 74(20), 4083–4086 (1995)

    Article  ADS  Google Scholar 

  2. Cirac, J.I.I., Zoller, P.: Quantum computations with cold trapped ions. Phys. Rev. Lett. 74(20), 4091–4094 (1995)

    Article  ADS  Google Scholar 

  3. Yi, X.X., Su, X.H., You, L.: Conditional quantum phase gate between two 3-state atoms. Phys. Rev. Lett. 90(9), 097902 (2003)

    Article  ADS  Google Scholar 

  4. Duan, L.-M., Kimble, H.J.: Scalable photonic quantum computation through cavity-assisted interactions. Phys. Rev. Lett. 92(12), 127902 (2004)

    Article  ADS  Google Scholar 

  5. Zou, X., Zhang, S.L., Li, K., Guo, G.: Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors. Phys. Rev. A 75(3), 034302 (2007)

    Article  ADS  Google Scholar 

  6. Wang, M.-F., Jiang, N.-Q., Jin, Q.-L., Zheng, Y.-Z.: Continuous-variable controlled-Z gate using an atomic ensemble. Phys. Rev. A 83(6), 062339 (2011)

    Article  ADS  Google Scholar 

  7. Nielsen, E., Muller, R., Carroll, M.: Configuration interaction calculations of the controlled phase gate in double quantum dot qubits. Phys. Rev. B 85(3), 035319 (2012)

    Article  ADS  Google Scholar 

  8. Wei, H.-R., Deng, F.-G.: Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities. Opt. Express 22(1), 593 (2014)

    Article  ADS  Google Scholar 

  9. Xu, G.F., Zhang, J., Tong, D.M., Sjöqvist, E., Kwek, L.C.: Nonadiabatic holonomic quantum computation in decoherence-free subspaces. Phys. Rev. Lett. 109(17), 170501 (2012)

    Article  ADS  Google Scholar 

  10. Xue, Z.-Y., Zhou, J., Wang, Z.D.: Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits. Phys. Rev. A 92(2), 022320 (2015)

    Article  ADS  Google Scholar 

  11. Schmidt-Kaler, F., Häffner, H., Riebe, M., Gulde, S., Lancaster, G.P., Deuschle, T., Becher, C., Roos, C.F., Eschner, J., Blatt, R.: Realization of the Cirac–Zoller controlled-NOT quantum gate. Nature 422(6930), 408–411 (2003)

    Article  ADS  Google Scholar 

  12. Turchette, Q.A., Hood, C.J., Lange, W., Mabuchi, H., Kimble, H.J.: Measurement of conditional phase shifts for quantum logic. Phys. Rev. Lett. 75(25), 4710–4713 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Lemr, K., Cernoch, A., Soubusta, J., Kieling, K., Eisert, J., Dusek, M.: Experimental implementation of the optimal linear-optical controlled phase gate. Phys. Rev. Lett. 106(1), 013602 (2011)

    Article  ADS  Google Scholar 

  14. Ukai, R., Yokoyama, S., Yoshikawa, J., van Loock, P., Furusawa, A.: Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation. Phys. Rev. Lett. 107(25), 250501 (2011)

    Article  ADS  Google Scholar 

  15. Rashid, M., Maarten, H., Yasir, J.: C-NOT gate based on ultracold Rydberg atom interactions. Sci. China 56(11), 2134–2137 (2013)

    Google Scholar 

  16. Feng, G., Guofu, X., Long, G.: Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110(19), 190501 (2013)

    Article  ADS  Google Scholar 

  17. Antonelli, C., Shtaif, M., Brodsky, M.: Sudden death of entanglement induced by polarization mode dispersion. Phys. Rev. Lett. 106(8), 080404 (2011)

    Article  ADS  Google Scholar 

  18. Shtaif, M., Antonelli, C., Brodsky, M.: Nonlocal compensation of polarization mode dispersion in the transmission of polarization entangled photons. Opt. Express 19(3), 1728–1733 (2011)

    Article  ADS  Google Scholar 

  19. Dong, L., Wang, J.-X., Li, Q.-Y., Shen, H.-Z., Dong, H.-K., Xiu, X.-M., Gao, Y.-J.: Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem. Opt. Lett. 41(5), 1030–1033 (2016)

    Article  ADS  Google Scholar 

  20. Nemoto, K., Munro, W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93(25), 250502 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. Lin, Q., He, B.: Single-photon logic gates using minimal resources. Phys. Rev. A 80(4), 042310 (2009)

    Article  ADS  Google Scholar 

  23. Xia, Y., Song, J., Pei-Min, L., Song, H.-S.: Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity. J. Phys. B Atomic Mol. Opt. Phys. 44(2), 025503 (2011)

    Article  ADS  Google Scholar 

  24. Lin, Q., He, B.: Weaving independently generated photons into an arbitrary graph state. Phys. Rev. A 84(6), 062312 (2011)

    Article  ADS  Google Scholar 

  25. Xiu, X.-M., Dong, L., Gao, Y.-J., Yi, X.X.: Nearly deterministic controlled-not gate with weak cross-Kerr nonlinearities. Quantum Inf. Comput. 12(1–2), 0159–0170 (2012)

    MathSciNet  MATH  Google Scholar 

  26. Xiu, X.-M., Dong, L., Shen, H.-Z., Gao, Y.-J., Yi, X.X.: Construction scheme of a two-photon polarization controlled arbitrary phase gate mediated by weak cross-phase modulation. J. Opt. Soc. Am. B 30(3), 589–597 (2013)

    Article  ADS  Google Scholar 

  27. Shende, V.V., Markov, I.L., Bullock, S.S.: Minimal universal two-qubit controlled-NOT-based circuits. Phys. Rev. A 69(6), 062321 (2004)

    Article  ADS  Google Scholar 

  28. Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theor. Phys. 21(3–4), 219–253 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  29. Chau, H.F., Wilczek, F.: Simple realization of the fredkin gate using a series of two-body operators. Phys. Rev. Lett. 75(4), 748–750 (1995)

    Article  ADS  Google Scholar 

  30. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457–3467 (1995)

    Article  ADS  Google Scholar 

  31. Sleator, T., Weinfurter, H.: Realizable universal quantum logic gates. Phys. Rev. Lett. 74(20), 4087–4090 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Smolin, J.A., DiVincenzo, D.P.: Five two-bit quantum gates are sufficient to implement the quantum Fredkin gate. Phys. Rev. A 53(4), 2855–2856 (1996)

    Article  ADS  Google Scholar 

  33. Nengkun, Y., Ying, M.: Optimal simulation of Deutsch gates and the Fredkin gate. Phys. Rev. A 91(3), 032302 (2015)

    Article  ADS  Google Scholar 

  34. Jones, C.: Low-overhead constructions for the fault-tolerant Toffoli gate. Phys. Rev. A 87(2), 022328 (2013)

    Article  ADS  Google Scholar 

  35. Ivanov, S.S., Ivanov, P.A., Vitanov, N.V.: Efficient construction of three- and four-qubit quantum gates by global entangling gates. Phys. Rev. A 91(3), 032311 (2015)

    Article  ADS  Google Scholar 

  36. Milburn, G.J.: Quantum optical Fredkin gate. Phys. Rev. Lett. 62(18), 2124–2127 (1989)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. Dong, L., Lin, Y.-F., Wang, J.-X., Li, Q.-Y., Shen, H.-Z., Dong, H.-K., Ren, Y.-P., Xiu, X.-M., Gao, Y.-J., Choo Hiap, O.: Nearly deterministic Fredkin gate based on weak cross-Kerr nonlinearities. J. Opt. Soc. Am. B 33(2), 253–260 (2016)

    Article  ADS  Google Scholar 

  39. Lin, X.-M., Zhou, Z.-W., Ye, M.-Y., Xiao, Y.-F., Guo, G.-C.: One-step implementation of a multiqubit controlled-phase-flip gate. Phys. Rev. A 73(1), 012323 (2006)

    Article  ADS  Google Scholar 

  40. Zou, X., Li, K., Guo, G.: Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate. Phys. Rev. A 74(4), 044305 (2006)

    Article  ADS  Google Scholar 

  41. Xiao, Y.-F., Zou, X.-B., Guo, G.-C.: One-step implementation of an N-qubit controlled-phase gate with neutral atoms trapped in an optical cavity. Phys. Rev. A 75(5), 054303 (2007)

    Article  ADS  Google Scholar 

  42. Zhang, Y.Q., Zhang, S., Yeon, K.H., Yu, S.C.: One-step implementation of a multiqubit controlled-phase gate with superconducting quantum interference devices coupled to a resonator. J. Opt. Soc. Am. B 29(3), 300–304 (2012)

    Article  ADS  Google Scholar 

  43. Xiu, X.-M., Li, Q.-Y., Lin, Y.-F., Dong, L., Dong, H.-K., Gao, Y.-J.: One-photon controlled two-photon not gate contributed by weak cross-Kerr nonlinearities. Opt. Commun. 393, 173–177 (2017)

    Article  ADS  Google Scholar 

  44. Gardiner, C.W., Zoller, P.: Quantum Noise. Springer Press, Berlin (2000)

    Book  MATH  Google Scholar 

  45. Hong, C.K., Ou, Z.Y., Mandel, L.: Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59(18), 2044–2046 (1987)

    Article  ADS  Google Scholar 

  46. Chuang, I., Yamamoto, Y.: Simple quantum computer. Phys. Rev. A 52(5), 3489–3496 (1995)

    Article  ADS  Google Scholar 

  47. Shapiro, J.: Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A 73(6), 062305 (2006)

    Article  ADS  Google Scholar 

  48. Shapiro, J.H., Razavi, M.: Continuous-time cross-phase modulation and quantum computation. N. J. Phys. 9(1), 16 (2007)

    Article  Google Scholar 

  49. Kok, P.: Effects of self-phase-modulation on weak nonlinear optical quantum gates. Phys. Rev. A 77(1), 013808 (2008)

    Article  ADS  MathSciNet  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(4), 043823 (2010)

    Article  ADS  Google Scholar 

  51. Fan, B., Kockum, A.F., Combes, J., Johansson, G., Hoi, I., Wilson, C.M., Delsing, P., Milburn, G.J., Stace, T.M.: Breakdown of the cross-Kerr scheme for photon counting. Phys. Rev. Lett. 110(5), 053601 (2013)

    Article  ADS  Google Scholar 

  52. Harris, S.E.: Electromagnetically induced transparency. Phys. Today 50(7), 36–42 (1997)

    Article  Google Scholar 

  53. Fleischhauer, M., Imamoglu, A., Marangos, J.P.: Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77(2), 633–673 (2005)

    Article  ADS  Google Scholar 

  54. Schmidt, H., Imamoglu, A.: Giant Kerr nonlinearities obtained by electromagnetically induced transparency. Opt. Lett. 21(23), 1936–1938 (1996)

    Article  ADS  Google Scholar 

  55. Harris, S., Hau, L.: Nonlinear optics at low light levels. Phys. Rev. Lett. 82(23), 4611–4614 (1999)

    Article  ADS  Google Scholar 

  56. Lukin, M.D., Imamoglu, A.: Nonlinear optics and quantum entanglement of ultraslow single photons. Phys. Rev. Lett. 84(7), 1419–1422 (2000)

    Article  ADS  Google Scholar 

  57. Petrosyan, D., Kurizki, G.: Symmetric photon–photon coupling by atoms with Zeeman-split sublevels. Phys. Rev. A 65(3), 033833 (2002)

    Article  ADS  Google Scholar 

  58. Bajcsy, M., Zibrov, A.S., Lukin, M.D.: Stationary pulses of light in an atomic medium. Nature 426(6967), 638–641 (2003)

    Article  ADS  Google Scholar 

  59. Chen, Y.-F., Wang, C.-Y., Wang, S.-H., Ite, A.Y.: Low-light-level cross-phase-modulation based on stored light pulses. Phys. Rev. Lett. 96(4), 043603 (2006)

    Article  ADS  Google Scholar 

  60. Li, Y., Hang, C., Ma, L., Huang, G.: Controllable entanglement of lights in a five-level system. Phys. Lett. A 354(1–2), 1–7 (2006)

    Article  ADS  Google Scholar 

  61. Wang, Z.-B., Marzlin, K.-P., Sanders, B.C.: Large cross-phase modulation between slow copropagating weak pulses in \(^{87}\)Rb. Phys. Rev. Lett. 97(6), 063901 (2006)

    ADS  Google Scholar 

  62. Lo, H.Y., Chen, Y.C., Su, P.C., Chen, H.C., Chen, J.X., Chen, Y.C., Yu, I.A., Chen, Y.F.: Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels. Phys. Rev. A 83(4), 041804(R) (2011)

    Article  ADS  Google Scholar 

  63. Shiau, B.-W., Meng-Chang, W., Lin, C.-C., Chen, Y.-C.: Low-light-level cross-phase modulation with double slow light pulses. Phys. Rev. Lett. 106(19), 193006 (2011)

    Article  ADS  Google Scholar 

  64. Chen, Y.H., Lee, M.J., Hung, W., Chen, Y.C., Chen, Y.F., Yu, I.A.: Demonstration of the interaction between two stopped light pulses. Phys. Rev. Lett. 108(17), 173603 (2012)

    Article  ADS  Google Scholar 

  65. Hau, L.V., Harris, S.E., Dutton, Z., Behroozi, C.H.: Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature 397(6720), 594–598 (1999)

    Article  ADS  Google Scholar 

  66. He, B., Lin, Q., Simon, C.: Cross-Kerr nonlinearity between continuous-mode coherent states and single photons. Phys. Rev. A 83(5), 053826 (2011)

    Article  ADS  Google Scholar 

  67. He, B., Scherer, A.: Continuous-mode effects and photon–photon phase gate performance. Phys. Rev. A 85(3), 033814 (2012)

    Article  ADS  Google Scholar 

  68. Friedler, I., Petrosyan, D., Fleischhauer, M., Kurizki, G.: Long-range interactions and entanglement of slow single-photon pulses. Phys. Rev. A 72(4), 043803 (2005)

    Article  ADS  Google Scholar 

  69. He, B., MacRae, A., Han, Y., Lvovsky, A., Simon, C.: Transverse multimode effects on the performance of photon–photon gates. Phys. Rev. A 83(2), 022312 (2011)

    Article  ADS  Google Scholar 

  70. Shahmoon, E., Kurizki, G., Fleischhauer, M., Petrosyan, D.: Strongly interacting photons in hollow-core waveguides. Phys. Rev. A 83(3), 033806 (2011)

    Article  ADS  Google Scholar 

  71. Venkataraman, V., Saha, K., Gaeta, A.L.: Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing. Nat. Photonics 7(2), 138–141 (2012)

    Article  ADS  Google Scholar 

  72. Jin, G.-S., Lin, Y., Biao, W.: Generating multiphoton Greenberger–Horne–Zeilinger states with weak cross-Kerr nonlinearity. Phys. Rev. A 75(5), 054302 (2007)

    Article  ADS  Google Scholar 

  73. Feizpour, A., Hallaji, M., Dmochowski, G., Steinberg, A.M.: Observation of the nonlinear phase shift due to single post-selected photons. Nat. Phys. 11(11), 905–909 (2015)

    Article  Google Scholar 

  74. Hoi, I.-C., Kockum, A.F., Palomaki, T., Stace, T.M., Fan, B., Tornberg, L., Sathyamoorthy, S.R., Johansson, G., Delsing, P., Wilson, C.M.: Giant cross-Kerr effect for propagating microwaves induced by an artificial atom. Phys. Rev. Lett. 111(5), 053601 (2013)

    Article  ADS  Google Scholar 

  75. Pernice, W.H.P., Schuck, C., Minaeva, O., Li, M., Goltsman, G.N., Sergienko, A.V., Tang, H.X.: High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits. Nat. Commun. 3, 1325 (2012)

    Article  ADS  Google Scholar 

  76. Huang, D., Huang, P., Lin, D., Wang, C., Zeng, G.: High-speed continuous-variable quantum key distribution without sending a local oscillator. Opt. Lett. 40(16), 3695–3698 (2015)

    Article  ADS  Google Scholar 

  77. Bakker, M.P., Snijders, H., Löffler, W., Barve, A.V., Coldren, L.A., Bouwmeester, D., van Exter, M.P.: Homodyne detection of coherence and phase shift of a quantum dot in a cavity. Opt. Lett. 40(13), 3173–3176 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant Nos. 11674037, 11544013, 11305016, 61301133, 11271055), the Natural Science Foundation of Liaoning Province (20170540010), the Program for Liaoning Innovative Talents in University (LR2016001), and the Program of the Educational Office of Liaoning Province of China (Grant No. LQ2017006).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Li Dong or Xiao-Ming Xiu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dong, L., Lin, YF., Cui, C. et al. Single-photon controlled multi-photon polarization unitary gate based on weak cross-Kerr nonlinearities. Quantum Inf Process 17, 114 (2018). https://doi.org/10.1007/s11128-018-1882-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1882-1

Keywords

Navigation