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Characterizing Bell state analyzer using weak coherent pulses


Bell state analyzer (BSA) is one of the most crucial apparatuses in photonic quantum information processing. While linear optics provide a practical way to implement BSA, it provides unavoidable errors when inputs are not ideal single-photon states. Here, we propose a simple method to deduce the BSA for single-photon inputs using weak coherent pulses. By applying the method to Reference-Frame-Independent Measurement-Device-Independent Quantum Key Distribution, we experimentally verify the feasibility and effectiveness of the method.

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  1. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2008)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  2. Branciard, C., Rosset, D., Liang, Y.-C., Gisin, N.: Measurement-device-independent entanglement witnesses for all entangled quantum states. Phys. Rev. Lett. 110, 060405 (2013)

    ADS  Article  Google Scholar 

  3. Kim, Y.-S., Pramanik, T., Cho, Y.-W., Yang, M., Han, S.-W., Lee, S.-Y., Kang, M.-S., Moon, S.: Informationally symmetrical Bell state preparation and measurement. Opt. Express 26, 29539 (2018)

    ADS  Article  Google Scholar 

  4. Braunstein, S.L., Pirandola, S.: Side-channel-free quantum key distribution. Phys. Rev. Lett. 108, 130502 (2012)

    ADS  Article  Google Scholar 

  5. Lo, H.-K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012)

    ADS  Article  Google Scholar 

  6. 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, 1895–1899 (1993)

    ADS  MathSciNet  Article  MATH  Google Scholar 

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

  8. Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390 (1999)

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  10. Gao, W.-B., Goebel, A.M., Lu, C.-Y., Dai, H.-N., Wagenknecht, C., Zhang, Q., Zhao, B., Peng, C.-Z., Chen, Z.-B., Chen, Y.-A., Pan, J.-W.: Teleportation-based realization of an optical quantum two-qubit entangling gate. Proc. Natl. Acad. Sci. USA 107, 20869 (2010)

    ADS  Article  Google Scholar 

  11. Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656 (1996)

    ADS  Article  Google Scholar 

  12. Ma, X.-S., Zotter, S., Kofler, J., Ursin, R., Jennewein, T., Brukner, C̆, Zeilinger, A.: Experimental delayed-choice entanglement swapping. Nature Phys. 8, 479 (2012)

  13. Calsamiglia, J., Lütkenhaus, N.: Maximum efficiency of a linear-optical Bell-state analyzer. Appl. Phys. B: Lasers and Opt. 72, 67 (2001)

    ADS  Article  Google Scholar 

  14. Choi, Y., Kwon, O., Woo, M., Oh, K., Han, S.-W., Kim, Y.-S., Moon, S.: Plug-and-play measurement-device-independent quantum key distribution. Phys. Rev. A 93, 032319 (2016)

    ADS  Article  Google Scholar 

  15. Yin, H.-L., Chen, T.-Y., Yu, Z.-W., Liu, H., You, L.-X., Zhou, Y.-H., Chen, S.-J., Mao, Y., Huang, M.-Q., Zhang, W.-J., Chen, H., Li, M. J., Nolan, D., F. Z., Jiang, X., Wang, Z., Zhang, Q., Wang, X.-B., Pan, J.-W.: Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys. Rev. Lett. 117, 190501 (2016)

  16. Park, C.H., Woo, M.K., Park, B.K., Lee, M.S., Kim, Y.-S., Cho, Y.-W., Kim, S., Han, S.-W., Moon, S.: Practical plug-and-play measurement-device- independent quantum key distribution with polarization division multiplexing. IEEE Access 6, 58587 (2018)

    Article  Google Scholar 

  17. Liu, H., Wang, W., Wei, K., Fang, X.-T., Li, L., Liu, N.-L., Liang, H., Zhang, S.-J., Zhang, W., Li, H., You, L., Wang, Z., Lo, H.-K., Chen, T.-Y., Xu, F., Pan, J.-W.: Experimental demonstration of high-rate measurement-device-independent quantum key distribution over asymmetric channels. Phys. Rev. Lett. 122, 160501 (2019)

    ADS  Article  Google Scholar 

  18. Wang, C., Song, X.-T., Yin, Z.-Q., Wang, S., Chen, W., Zhang, C.-M., Guo, G.-C., Han, Z.-F.: Phase-reference-free experiment of measurement-device-independent quantum key distribution. Phys. Rev. Lett. 115, 160502 (2015)

    ADS  Article  Google Scholar 

  19. Wang, C., Yin, Z.-Q., Wang, S., Chen, W., Guo, G.-C., Han, Z.-F.: Measurement-device-independent quantum key distribution robust against environmental disturbances. Optica 4, 1016 (2017)

    ADS  Article  Google Scholar 

  20. Liu, H., Wang, J., Ma, H., Sun, S.: Polarization-multiplexing-based measurement-device-independent quantum key distribution without phase reference calibration. Optica 5, 902 (2018)

    ADS  Article  Google Scholar 

  21. Yuan, X., Zhang, Z., Lütkenhaus, Norbert, Ma, X.: Simulating single photons with realistic photon sources. Phys. Rev. A 94, 062305 (2016)

  22. Navarrete, Á., Wang, W., Xu, F., Curty, M.: Characterizing multi-photon quantum interference with practical light sources and threshold single-photon detectors. New J. Phys. 20, 043018 (2018)

    ADS  Article  Google Scholar 

  23. Aragoneses, A., Islam, N.T., Eggleston, M., Lezama, A., Kim, J., Gauthier, D.J.: Bounding the outcome of a two-photon interference measurement using weak coherent states. Opt. Lett. 43, 3806 (2018)

    ADS  Article  Google Scholar 

  24. Zhang, Y.-Z., Wei, K., Xu, F.: Generalized Hong-Ou-Mandel quantum interference with phase-randomized weak coherent states. Phys. Rev. A 101, 033823 (2020)

    ADS  Article  Google Scholar 

  25. Lee, D., Hong, S.-J., Cho, Y.-W., Lim, H.-T., Han, S.-W., Jung, H., Moon, S., Lee, K.J., Kim, Y.-S.: Reference-frame-independent measurement-device-independent quantum key distribution using fewer quantum states. Opt. Lett. 45, 2624 (2020)

    ADS  Article  Google Scholar 

  26. Kim, Y.-S., Slattery, O., Kuo, P.S., Tang, X.: Conditions for two-photon interference with coherent pulses. Phys. Rev. A 87, 063843 (2013)

    ADS  Article  Google Scholar 

  27. Kim, Y.-S., Slattery, O., Kuo, P.S., Tang, X.: Two-photon interference with continuous-wave multi-mode coherent light. Opt. Express 22, 3611 (2014)

    ADS  Article  Google Scholar 

  28. Yoon, J., Pramanik, T., Park, B.-K., Cho, Y.-W., Lee, S.-Y., Kim, S., Han, S.-W., Moon, S., Kim, Y.-S.: Experimental comparison of various quantum key distribution protocols under reference frame rotation and fluctuation. Opt. Comm. 441, 64 (2019)

    ADS  Article  Google Scholar 

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This work was supported by the NRF programs (2019M3E4A1079777, 2019R1A2C2006381, 2019M3E4A107866011), the IITP programs (2020-0-00947, 2020-0-00972), and the KIST research program (2E30620).

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Correspondence to Yong-Su Kim.

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Lee, D., Cho, YW., Lim, HT. et al. Characterizing Bell state analyzer using weak coherent pulses. Quantum Inf Process 20, 149 (2021).

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  • Linear optical quantum circuits
  • Bell state analyzer
  • Photon number distribution
  • Photonic qubits