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Entanglement concentration of W state using linear optics with a higher success probability

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Abstract

Entanglement concentration protocol (ECP), as a practical technique, can be use to preclude degraded fidelity and improve security in long-haul quantum communication. We propose an efficient ECP for less-entangled unknown W states with simple linear-optics elements and effective single-photon detectors, resorting to time-delay degree of freedom. Moreover, in contrast to previous ECPs proposed for W states, the scheme has the advantages over requiring less quantum resource without auxiliary photons, comparatively simplified circuits, involving neither post-selection techniques nor photon-number-resolving detectors to distinguish the parity outcome, and being provided with a higher success probability by reusing the less-entangled states.

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References

  1. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Am. J. Phys. 70, 558 (2002)

    ADS  Google Scholar 

  2. Wu, Y.M., Fan, G., Du, F.F.: Error-detected three-photon hyperparallel Toffoli gate with state-selective reflection. Front. Phys. 17, 51502 (2022)

    ADS  Google Scholar 

  3. Du, F.F., Ma, M., Ren, X.M., Fan, G., Du, X.S., Li, L.H., Fan, Z.G., Guo, J.: Deterministic conversion of hyperentangled states with error-heralded quantum units. Ann. Phys. 2300455 (2024)

  4. Cao, C., Zhang, L., Han, Y.H., Yin, P.P., Fan, L., Duan, Y.W., Zhang, R.: Complete and faithful hyperentangled-Bell-state analysis of photon systems using a failure-heralded and fidelity-robust quantum gate. Opt. Express 28, 2857 (2020)

    ADS  Google Scholar 

  5. Du, F.F., Ren, X.M., Fan, Z.G., Li, L.H., Du, X.S., Ma, M., Fan, G., Guo, J.: Decoherence-free-subspace-based deterministic conversions for entangled states with heralded robust-fidelity quantum gates. Opt. Express 32, 1686 (2024)

    ADS  Google Scholar 

  6. Zhou, Y.R., Zhang, Q.F., Liu, F.F., Han, Y.H., Gao, Y.P., Fan, L., Zhang, R., Cao, C.: Controllable nonreciprocal phonon laser in a hybrid photonic molecule based on directional quantum squeezing. Opt. Express 32, 2786 (2024)

    ADS  Google Scholar 

  7. Li, T., Wang, Z.K., Xia, K.Y.: Multipartite quantum entanglement creation for distant stationary systems. Opt. Express 28, 1316 (2020)

    ADS  Google Scholar 

  8. Du, F.F., Ren, X.M., Ma, M., Fan, G.: Complete conversion of KLM entanglement to GHZ entanglement with error-detected quantum devices. Appl. Phys. Express 16, 102006 (2023)

    ADS  Google Scholar 

  9. Han, Y.H., Cao, C., Fan, L., Zhang, R.: Heralded high-fidelity quantum hyper-CNOT gates assisted by charged quantum dots inside single-sided optical microcavities. Opt. Express 29, 20045 (2021)

    ADS  Google Scholar 

  10. Du, F.F., Wu, Y.M., Fan, G.: Refined quantum gates for \(\Lambda \)-type atom-photon hybrid systems. Adv. Quantum Technol. 6, 2300090 (2023)

    Google Scholar 

  11. Du, F.F., Wu, Y.M., Fan, G., Ma, Z.M.: High-fidelity and low-cost hyperparallel quantum gates for photon systems via \(\Lambda \)-type systems. Ann. Phys. 535, 2200507 (2023)

    Google Scholar 

  12. Zhang, XYu., Cao, C., Gao, Y.P., Fan, L., Zhang, R., Wang, C.: Generation and manipulation of phonon lasering in a two-drive cavity magnomechanical system. New J. Phys. 25, 053039 (2023)

    ADS  Google Scholar 

  13. Du, F.F., Fan, G., Wu, Y.M.: Implementations of heralded quantum Toffoli and Fredkin gates assisted by waveguide-mediated photon scattering. Quantum Inf. Process 22, 55 (2023)

    ADS  MathSciNet  Google Scholar 

  14. Du, F.F., Shi, Z.R.: Robust hybrid hyper-controlled-not gates assisted by an input-output process of low-Q cavities. Opt. Express 27, 17493 (2019)

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  16. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560, 7 (2014)

    MathSciNet  Google Scholar 

  17. Kwek, L.C., Cao, L., Luo, W., Wang, Y.X., Sun, S.H., Wang, X.B., Liu, A.Q.: Chip-based quantum key distribution. AAPPS Bull. 31, 15 (2021)

    ADS  Google Scholar 

  18. Huang, J.S., Chen, X.J., Li, X.D., Wang, J.W.: Chip-based photonic graph states. AAPPS Bull. 33, 14 (2023)

    ADS  Google Scholar 

  19. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    ADS  MathSciNet  Google Scholar 

  20. Liu, X.S., Long, G.L., Tong, D.M., Li, F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65, 022304 (2002)

    ADS  Google Scholar 

  21. Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  23. Li, T., Long, G.L.: Quantum secure direct communication based on single-photon Bell-state measurement. New J. Phys. 22, 063017 (2020)

    ADS  MathSciNet  Google Scholar 

  24. Qi, Z.T., Li, Y.H., Huang, Y.W., Feng, J., Zheng, Y.L., Chen, X.F.: A 15-user quantum secure direct communication network. Light Sci. Appl. 10, 183 (2021)

    ADS  Google Scholar 

  25. Long, G.L., Zhang, H.R.: Drastic increase of channel capacity in quantum secure direct communication using masking. Sci. Bull. 66, 1267 (2021)

    Google Scholar 

  26. Sheng, Y.B., Zhou, L., Long, G.L.: One-step quantum secure direct communication. Sci. Bull. 67, 367 (2022)

    Google Scholar 

  27. Chen, S.S., Zhou, L., Zhong, W., Sheng, Y.B.: Three-step three-party quantum secure direct communication. Sci. China Phys. Mech. 61, 90312 (2018)

    Google Scholar 

  28. Wu, X.D., Zhou, L., Zhong, W., Sheng, Y.B.: High-capacity measurement-device-independent quantum secure direct communication. Quantum Inf. Process. 19, 354 (2020)

    ADS  MathSciNet  Google Scholar 

  29. Hong, Y.P., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-device-independent three-party quantum secure direct communication. Quantum Inf. Process. 22, 111 (2023)

    ADS  MathSciNet  Google Scholar 

  30. Cao, Z.W., Lu, Y., Chai, G., Yu, H., Liang, K.X., Wang, L.: Realization of quantum secure direct communication with continuous variable. Research 6, 0193 (2023)

    Google Scholar 

  31. Pan, D., Song, X.T., Long, G.L.: Free-space quantum secure direct communication: basics, progress, and outlook. Adv. Devices Instrum. 4, 0004 (2023)

    Google Scholar 

  32. Wu, J.W., Long, G.L., Hayashi, M.: Quantum secure direct communication with private dense coding using a general preshared quantum state. Phys. Rev. Appl. 17, 064011 (2022)

    ADS  Google Scholar 

  33. Li, X.J., Pan, D., Long, G.L., Hanzo, L.: Single-photon-memory measurement-device-independent quantum secure direct communication-part I: its fundamentals and evolution. IEEE Commun. Lett. 27, 1055 (2023)

    Google Scholar 

  34. Li, X.J., Pan, D., Long, G.L., Hanzo, L.: Single-photon-memory measurement-device-independent quantum secure direct communication-part II: a practical protocol and its secrecy capacity. IEEE Commun. Lett. 27, 1060 (2023)

    Google Scholar 

  35. Sun, Z.Z., Pan, D., Ruan, D., Long, G.L.: One-sided measurement-device-independent practical quantum secure direct communication. J. Light. 41, 4680 (2023)

    Google Scholar 

  36. Cao, C., Duan, Y.W., Chen, X., Zhang, R., Wang, T.J., Wang, C.: Implementation of single-photon quantum routing and decoupling using a nitrogen-vacancy center and a whispering-gallery-mode resonator-waveguide system. Opt. Express 25, 16931 (2017)

    ADS  Google Scholar 

  37. Wang, B.X., Tao, M.J., Ai, Q., Xin, T., Lambert, N., Ruan, D., Cheng, Y.C., Nori, F., Deng, F.G., Long, G.L.: Efficient quantum simulation of photosynthetic light harvesting. NPJ Quantum Inf. 4, 52 (2018)

    ADS  Google Scholar 

  38. Jiang, G.L., Yuan, J.B., Liu, W.Q., Wei, H.R.: Efficient and deterministic high-dimensional controlled-swap gates on hybrid linear optical systems with high fidelity. Phys. Rev. Appl. 21, 014001 (2024)

    ADS  Google Scholar 

  39. Ai, Q., Li, P.B., Qin, W., Zhao, J.X., Sun, C.P., Nori, F.: The NV metamaterial: tunable quantum hyperbolic metamaterial using nitrogen vacancy centers in diamond. Phys. Rev. B 22, 014109 (2021)

    ADS  Google Scholar 

  40. Liu, W.Q., Wei, H.R.: Linear optical universal quantum gates with higher success probabilities. Adv. Quantum Technol. 6, 2300009 (2023)

    Google Scholar 

  41. Liu, W.Q., Wei, H.R., Kwek, L.C.: Universal quantum multi-qubit entangling gates with auxiliary spaces. Adv. Quantum Technol. 5, 2100136 (2022)

    Google Scholar 

  42. Liu, W.Q., Wei, H.R.: Optimal synthesis of the Fredkin gate in a multilevel system. New J. Phys. 22, 063026 (2020)

    ADS  MathSciNet  Google Scholar 

  43. Liu, W.Q., Wei, H.R., Kwek, L.C.: Low-cost Fredkin gate with auxiliary space. Phys. Rev. Appl. 14, 054057 (2020)

    ADS  Google Scholar 

  44. Huang, H.L., Xu, X.Y., Guo, C., Tian, G.J., Wei, S.J., Sun, X.M., Bao, W.S., Long, G.L.: Near-term quantum computing techniques: variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation. Sci. China Phys. Mech 66, 250302 (2023)

    Google Scholar 

  45. Long, G.L., Pan, D., Sheng, Y.B., Xue, Q.K., Lu, J.H., Hanzo, L.: An evolutionary pathway for the quantum internet relying on secure classical repeaters. IEEE Netw. 36, 82 (2022)

    Google Scholar 

  46. Du, F.F., Ren, X.M., Ma, M., F, G.: Qudit-based high-dimensional controlled-not gate. Opt. Lett. 49, 1229–1232 (2024)

  47. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722 (1996)

    ADS  Google Scholar 

  48. Du, F.F., Liu, Y.T., Shi, Z.R., Liang, Y.X., Tang, J., Liu, J.: Efficient hyperentanglement purification for three-photon systems with the fidelity-robust quantum gates and hyperentanglement link. Opt. Express 27, 27046 (2019)

    ADS  Google Scholar 

  49. Yan, P.S., Zhou, L., Zhong, W., Sheng, Y.B.: Feasible measurement-based entanglement purification in linear optics. Opt. Express 29, 9363 (2021)

    ADS  Google Scholar 

  50. Yan, P.S., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-based entanglement purification for entangled coherent states. Front. Phys. 17, 21501 (2022)

    ADS  Google Scholar 

  51. Huang, C.X., Hu, X.M., Liu, B.H., Zhou, L., Sheng, Y.B., Li, C.F., Guo, G.C.: Experimental one-step deterministic polarization entanglement purification. Sci. Bull. 67, 593 (2022)

    Google Scholar 

  52. Yan, P.S., Zhou, L., Zhong, W., Sheng, Y.B.: Advances in quantum entanglement purification. Sci. China Phys. Mech. 66, 250301 (2023)

    Google Scholar 

  53. Wang, P., Zhang, Z., Yu, C.Q., Yuan, R.Y., Du, F.F., Ren, B.C.: Measurement-based hyperentanglement distillation for lossy and distortion photon state. Ann. Phys. 535, 2200505 (2023)

    Google Scholar 

  54. Wu, X.D., Zhou, L., Zhong, W., Sheng, Y.B.: Purification of the concatenated Greenberger-Horne-Zeilinger state with linear optics. Quantum Inf. Process. 17, 255 (2018)

    ADS  MathSciNet  Google Scholar 

  55. Zhou, L., Liu, Z.K., Xu, Z.X., Cui, Y.L., Ran, H.J., Sheng, Y.B.: Economical multi-photon polarization entanglement purification with Bell state. Quantum Inf. Process. 20, 257 (2021)

    ADS  MathSciNet  Google Scholar 

  56. Luo, C.C., Zhou, L., Zhong, W., Sheng, Y.B.: Purification for hybrid logical qubit entanglement. Quantum Inf. Process. 21, 300 (2022)

    ADS  MathSciNet  Google Scholar 

  57. Zhou, L., Zhong, W., Sheng, Y.B.: Purification of the residual entanglement. Opt. Express 28, 2291 (2020)

    ADS  Google Scholar 

  58. Wang, P., Yu, C.Q., Wang, Z.X., Yuan, R.Y., Du, F.F., Ren, B.C.: Hyperentanglement-assisted hyperdistillation for hyper-encoding photon system. Front. Phys. 17, 31501 (2021)

    ADS  Google Scholar 

  59. Du, F.F., Fan, G., Wu, Y.M., Ren, B.C.: Faithful and efficient hyperentanglement purification for spatial-polarization-time-bin photon system. Chin. Phys. B 32, 060304 (2023)

    ADS  Google Scholar 

  60. Fan, G., Ren, X.M., Du, F.F.: Compact entanglement concentration for three-electron-spin W states with error-detected parity-check gates. Laser Phys. 33, 085202 (2023)

    ADS  Google Scholar 

  61. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    ADS  Google Scholar 

  62. Zhao, Z., Pan, J.W., Zhan, M.S.: Practical scheme for entanglement concentration. Phys. Rev. A 64, 014301 (2001)

    ADS  Google Scholar 

  63. Ren, B.C., Long, G.L.: General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities. Opt. Express 22, 6547 (2014)

    ADS  Google Scholar 

  64. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A 77, 062325 (2008)

    ADS  Google Scholar 

  65. Sheng, Y.B., Zhou, L., Zhao, S.M., Zheng, B.Y.: Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85, 012307 (2012)

    ADS  Google Scholar 

  66. Deng, F.G.: Optimal nonlocal multipartite entanglement concentration based on projection measurements. Phys. Rev. A 85, 022311 (2012)

    ADS  Google Scholar 

  67. Han, K.Q., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-device-independent quantum dialogue based on hyperentanglement. Quantum Inf. Process. 20, 280 (2021)

    ADS  MathSciNet  Google Scholar 

  68. Li, Y.P., Zhang, J., Xu, B.W., Zhou, L., Zhong, W., Sheng, Y.B.: Entanglement-assisted noiseless linear amplification for arbitrary two-photon polarization-time-bin hyperentanglement. Quantum Inf. Process. 19, 261 (2020)

    ADS  MathSciNet  Google Scholar 

  69. Takashi, Y., Masato, K., Nobuyuki, I.: Concentration and purification scheme for two partially entangled photon pairs. Phys. Rev. A 64, 022311 (2001)

    Google Scholar 

  70. Yang, G., Zhang, Y.S., Yang, Z.R., Zhou, L., Sheng, Y.B.: Linear-optical heralded amplification protocol for two-photon spatial-mode-polarization hyperentangled state. Quantum Inf. Process. 18, 317 (2019)

    ADS  MathSciNet  Google Scholar 

  71. Du, F.F., Fan, G., Ren, X.M., Ma, M.: Deterministic hyperparallel control gates with weak kerr effects. Adv. Quantum Technol. 6, 2300201 (2023)

    Google Scholar 

  72. Zheng, Y.B., Zhou, X.J., Wei, H.R., Du, F.F., Song, G.Z.: Schemes for fusing photonic W-state simultaneously without qubit loss via weak cross-Kerr nonlinearities. Quantum Inf. Process. 20, 273 (2021)

    ADS  MathSciNet  Google Scholar 

  73. Du, F.F., Fan, G., Wu, Y.M.: Refined Fredkin gate assisted by cross-Kerr nonlinearity. Opt. Commun 546, 129795 (2023)

    Google Scholar 

  74. Jiang, G.L., Liu, W.Q., Wei, H.R.: Heralded and high-efficient entanglement concentrations based on linear optics assisted by time-delay degree of freedom. Opt. Express 30, 47836 (2022)

    ADS  Google Scholar 

  75. Jiang, G.L., Liu, W.Q., Wei, H.R.: Practically enhanced hyperentanglement concentration for polarization-spatial hyperentangled bell states with linear optics and common single-photon detectors. Phys. Rev. A 19, 034044 (2023)

    Google Scholar 

  76. Ren, B.C., Du, F.F., Deng, F.G.: Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys. Rev. A 88, 012302 (2013)

    ADS  Google Scholar 

  77. Zhou, X.J., Liu, W.Q., Zheng, Y.B., Wei, H.R., Du, F.F.: Complete hyperentangled bell states analysis for polarization-spatial-time-bin degrees of freedom with unity fidelity. Ann. Phys. 534, 2100509 (2022)

    MathSciNet  Google Scholar 

  78. Ding, S.P., Zhou, L., Zhong, W., Sheng, Y.B.: Construction of quantum gates for concatenated Greenberger-Horne-Zeilinger-type logic qubit. Quantum Inf. Process. 17, 306 (2018)

    ADS  MathSciNet  Google Scholar 

  79. Zhou, X.J., Liu, W.Q., Wei, H.R., Zheng, Y.B., Du, F.F.: Deterministic and complete hyperentangled Bell states analysis assisted by frequency and time interval degrees of freedom. Front. Phys. 17, 41502 (2022)

    ADS  Google Scholar 

  80. Xu, J.S., Li, C.F.: Quantum integrated circuit: classical characterization. Sci. Bull. 60, 141 (2015)

    Google Scholar 

  81. Cao, C., Chen, X., Duan, Y.W., Fan, L., Zhang, R., Wang, T.J., Wang, C.: Concentrating partially entangled W-class states on nonlocal atoms using low-Q optical cavity and linear optical elements. Sci. China Phys. Mech. 59, 100315 (2016)

    Google Scholar 

  82. Sheng, Y.B., Pan, J., Guo, R., Zhou, L., Wang, L.: Efficient N-particle W state concentration with different parity check gates. Sci. China Phys. Mech. 58, 060301 (2015)

    Google Scholar 

  83. Du, F.F., Deng, F.G.: Heralded entanglement concentration for photon systems with linear-optical elements. Sci. China Phys. Mech. 58, 040303 (2015)

    Google Scholar 

  84. Sheng, Y.B., Zhou, L., Zhao, S.M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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  1. Science and Technology on Electronic Test and Measurement Laboratory, North University of China, Taiyuan, 030051, China

    Fang-Fang Du, Ming Ma, Xue-Mei Ren & Gang Fan

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  1. Fang-Fang Du
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Du, FF., Ma, M., Ren, XM. et al. Entanglement concentration of W state using linear optics with a higher success probability. Quantum Inf Process 23, 134 (2024). https://doi.org/10.1007/s11128-024-04334-9

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