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Faithful quantum entanglement purification and concentration using heralded high-fidelity parity-check detectors based on quantum-dot-microcavity systems

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Abstract

Entanglement purification and concentration are effective means to deal with the influence of noise on the coherence of entangled quantum systems, which enable us to carry out secure and efficient quantum communications. However, the reliability of parity check in parity-check-based entanglement purification and concentration schemes will inevitably affect the performance of the schemes. In this paper, we propose faithful entanglement purification and concentration schemes for polarization-entangled photon pairs, using heralded high-fidelity parity-check detectors (PCDs) constructed by double-sided quantum-dot-microcavity (QD-microcavity) systems and linear-optical elements. The PCD is based on the general interaction rule between the input photon and the QD-microcavity system, without the requirement of the system to strictly satisfy the specifically ideal conditions for giant circular birefringence, which makes it more realizable in practice. Moreover, the PCD can work in a failure-heralded and fidelity-robust fashion, so it can make a correct judgement on the parity mode of a two-photon system and has no destruction on the entangled state. Our schemes can therefore realize faithful entanglement purification and concentration by utilizing the PCD, without reducing the fidelity and entanglement degree of the obtained entangled-state ensemble. These features make our schemes more feasible and useful in quantum repeaters and quantum networks.

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References

  1. Nielsen, M.A., Chuang, I.: Quantum Computation and Quantum Information. American Association of Physics Teachers (2002)

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  4. Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69(20), 2881 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Liu, X., Long, G., Tong, D., Li, F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65(4), 022304 (2002)

    Article  ADS  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(13), 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block. Phys. Rev. A 68(4), 042317 (2003)

    Article  ADS  Google Scholar 

  8. Zhang, W., Ding, D.S., Sheng, Y.B., Zhou, L., Shi, B.S., Guo, G.C.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118(22), 220501 (2017)

    Article  ADS  Google Scholar 

  9. Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86(22), 5188 (2001)

    Article  ADS  Google Scholar 

  10. Briegel, H.J., Dür, W., Cirac, J.I., Zoller, P.: Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81(26), 5932 (1998)

    Article  ADS  Google Scholar 

  11. Duan, L.M., Lukin, M., Cirac, J.I., Zoller, P.: Long-distance quantum communication with atomic ensembles and linear optics. Nature 414(6862), 413 (2001)

    Article  ADS  Google Scholar 

  12. 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(5), 722 (1996)

    Article  ADS  Google Scholar 

  13. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53(4), 2046 (1996)

    Article  ADS  Google Scholar 

  14. Pan, J.W., Simon, C., Brukner, Č, Zeilinger, A.: Entanglement purification for quantum communication. Nature 410(6832), 1067 (2001)

    Article  ADS  Google Scholar 

  15. Pan, J.W., Gasparoni, S., Ursin, R., Weihs, G., Zeilinger, A.: Experimental entanglement purification of arbitrary unknown states. Nature 423(6938), 417 (2003)

    Article  ADS  Google Scholar 

  16. Simon, C., Pan, J.W.: Polarization entanglement purification using spatial entanglement. Phys. Rev. Lett. 89(25), 257901 (2002)

    Article  ADS  Google Scholar 

  17. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys. Rev. A 77(4), 042308 (2008)

    Article  ADS  Google Scholar 

  18. Sheng, Y.B., Deng, F.G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81(3), 032307 (2010)

    Article  ADS  Google Scholar 

  19. Sheng, Y.B., Deng, F.G.: One-step deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82(4), 044305 (2010)

    Article  ADS  Google Scholar 

  20. Deng, F.G.: One-step error correction for multipartite polarization entanglement. Phys. Rev. A 83(6), 062316 (2011)

    Article  ADS  Google Scholar 

  21. Zhou, L., Zhong, W., Sheng, Y.B.: Purification of the residual entanglement. Opt. Express 28(2), 2291 (2020)

    Article  ADS  Google Scholar 

  22. Yan, P.S., Zhou, L., Zhong, W., Sheng, Y.B.: Feasible measurement-based entanglement purification in linear optics. Opt. Express 29(6), 9363 (2021)

    Article  ADS  Google Scholar 

  23. Yan, P.S., Zhou, L., Zhong, W., Sheng, Y.B.: Feasible time-bin entanglement purification based on sum-frequency generation. Opt. Express 29(2), 571 (2021)

    Article  ADS  Google Scholar 

  24. Hu, X.M., Huang, C.X., Sheng, Y.B., Zhou, L., Liu, B.H., Guo, Y., Zhang, C., Xing, W.B., Huang, Y.F., Li, C.F., et al.: Long-distance entanglement purification for quantum communication. Phys. Rev. Lett. 126(1), 010503 (2021)

    Article  ADS  Google Scholar 

  25. Bose, S., Vedral, V., Knight, P.: Purification via entanglement swapping and conserved entanglement. Phys. Rev. A 60(1), 194 (1999)

    Article  ADS  Google Scholar 

  26. Shi, B.S., Jiang, Y.K., Guo, G.C.: Optimal entanglement purification via entanglement swapping. Phys. Rev. A 62(5), 054301 (2000)

    Article  ADS  Google Scholar 

  27. Zhao, Z., Pan, J.W., Zhan, M.S.: Practical scheme for entanglement concentration. Phys. Rev. A 64(1), 14301 (2001)

    Article  ADS  Google Scholar 

  28. Yamamoto, T., Koashi, M., Imoto, N.: Concentration and purification scheme for two partially entangled photon pairs. Phys. Rev. A 64(1), 012304 (2001)

    Article  ADS  Google Scholar 

  29. Zhao, Z., Yang, T., Chen, Y.A., Zhang, A.N., Pan, J.W.: Experimental realization of entanglement concentration and a quantum repeater. Phys. Rev. Lett. 90(20), 207901 (2003)

    Article  ADS  Google Scholar 

  30. Yamamoto, T., Koashi, M., Ozdemir, S.K., Imoto, N.: Experimental extraction of an entangled photon pair from two identically decohered pairs. Nature 421, 343–346 (2003)

    Article  ADS  Google Scholar 

  31. 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(6), 062325 (2008)

    Article  ADS  Google Scholar 

  32. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Single-photon entanglement concentration for long-distance quantum communication. Quantum Inf. Comput. 10(3), 272–281 (2010)

    MathSciNet  MATH  Google Scholar 

  33. 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(1), 012307 (2012)

    Article  ADS  Google Scholar 

  34. Deng, F.G.: Optimal nonlocal multipartite entanglement concentration based on projection measurements. Phys. Rev. A 85(2), 022311 (2012)

    Article  ADS  Google Scholar 

  35. Sheng, Y.B., Zhou, L.: Quantum entanglement concentration based on nonlinear optics for quantum communications. Entropy 15(5), 1776 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Du, F., Deng, F.: Heralded entanglement concentration for photon systems with linear-optical elements. Sci. China Phys. Mech. Astron. 58(4), 1–8 (2015)

    Article  Google Scholar 

  37. Wang, C., Zhang, Y., Jin, G.S., Zhang, R.: Efficient entanglement purification of separate nitrogen-vacancy centers via coupling to microtoroidal resonators. JOSA B 29(12), 3349 (2012)

    Article  ADS  Google Scholar 

  38. Cao, C., Wang, C., He, L.Y., Zhang, R.: Atomic entanglement purification and concentration using coherent state input–output process in low-Q cavity QED regime. Opt. Express 21(4), 4093 (2013)

    Article  ADS  Google Scholar 

  39. Ren, B.C., Deng, F.G.: Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities. Laser Phys. Lett. 10(11), 115201 (2013)

    Article  ADS  Google Scholar 

  40. Zhang, H., Liu, Q., Xu, X.S., Xiong, J., Alsaedi, A., Hayat, T., Deng, F.G., et al.: Polarization entanglement purification of nonlocal microwave photons based on the cross-Kerr effect in circuit QED. Phys. Rev. A 96(5), 052330 (2017)

    Article  ADS  Google Scholar 

  41. Liu, A.P., Guo, Q., Su, S.L., Cheng, L.Y., Wang, H.F., Zhang, S.: Entanglement purification on separate atoms in an error-detected pattern. Int. J. Theor. Phys. 58(5), 1404–1417 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  42. Lu, L.C., Wang, G.Y., Ren, B.C., Zhang, M., Deng, F.G.: Heralded entanglement purification protocol using high-fidelity parity-check gate based on nitrogen-vacancy center in optical cavity. Chin. Phys. B 29(1), 010305 (2020)

    Article  ADS  Google Scholar 

  43. Yang, M., Zhao, Y., Song, W., Cao, Z.L.: Entanglement concentration for unknown atomic entangled states via entanglement swapping. Phys. Rev. A 71(4), 044302 (2005)

    Article  ADS  Google Scholar 

  44. Peng, Z.H., Zou, J., Liu, X.J., Xiao, Y.J., Kuang, L.M.: Atomic and photonic entanglement concentration via photonic Faraday rotation. Phys. Rev. A 86(3), 034305 (2012)

    Article  ADS  Google Scholar 

  45. Sheng, Y., Liu, J., Zhao, S., Zhou, L.: Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system. Chin. Sci. Bull. 58(28), 3507 (2013)

    Article  Google Scholar 

  46. Cao, C., Chen, X., Duan, Y., Fan, L., Zhang, R., Wang, T., Wang, C.: Concentrating partially entangled W-class states on nonlocal atoms using low-Q optical cavity and linear optical elements. Sci. China Phys. Mech. Astron. 59(10), 100315 (2016)

    Article  Google Scholar 

  47. Petta, J.R., Johnson, A.C., Taylor, J.M., Laird, E.A., Yacoby, A., Lukin, M.D., Marcus, C.M., Hanson, M.P., Gossard, A.C.: Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309(5744), 2180 (2005)

    Article  ADS  Google Scholar 

  48. Hofheinz, M., Jehl, X., Sanquer, M., Molas, G., Vinet, M., Deleonibus, S.: Individual charge traps in silicon nanowires. Eur. Phys. J. B-Condens. Matter Complex Syst. 54(3), 299 (2006)

    Article  Google Scholar 

  49. Lodahl, P., Mahmoodian, S., Stobbe, S.: Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87(2), 347 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  50. Hu, C.Y., Young, A., O’rien, J., Munro, W., Rarity, J.: Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: applications to entangling remote spins via a single photon. Phys. Rev. B 78(8), 085307 (2008)

    Article  ADS  Google Scholar 

  51. Hu, C.Y., Munro, W., O’rien, J., Rarity, J.: Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity. Phys. Rev. B 80(20), 205326 (2009)

    Article  ADS  Google Scholar 

  52. Bonato, C., Haupt, F., Oemrawsingh, S.S., Gudat, J., Ding, D., van Exter, M.P., Bouwmeester, D.: CNOT and Bell-state analysis in the weak-coupling cavity QED regime. Phys. Rev. Lett. 104(16), 160503 (2010)

    Article  ADS  Google Scholar 

  53. Wei, H.R., Deng, F.G.: Scalable quantum computing based on stationary spin qubits in coupled quantum dots inside double-sided optical microcavities. Sci. Rep. 4(1), 7551 (2014)

    Article  Google Scholar 

  54. Wang, G.Y., Li, T., Ai, Q., Deng, F.G.: Self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom. Opt. Express 26(18), 23333 (2018)

    Article  ADS  Google Scholar 

  55. Xu, W.L., Wang, T.J., Cao, C., Wang, C.: High dimensional quantum logic gates and quantum information processing (in Chinese). Chin. Sci. Bull. 64(16), 1691–1701 (2019)

    Article  Google Scholar 

  56. Wang, G.Y., Ai, Q., Ren, B.C., Li, T., Deng, F.G.: Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities. Opt. Express 24(25), 28444 (2016)

    Article  ADS  Google Scholar 

  57. 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(3), 2857 (2020)

    Article  ADS  Google Scholar 

  58. Wang, C., Zhang, Y., Jin, G.S.: Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A 84(3), 5200 (2011)

    Article  Google Scholar 

  59. Liu, Z.C., Hong, J.S., Guo, J.J., Li, T., Ai, Q., Alsaedi, A., Hayat, T., Deng, F.G.: Entanglement purification of nonlocal quantum-dot-confined electrons assisted by double-sided optical microcavities. Ann. Phys. 530(4), 1800029 (2018)

    Article  MathSciNet  Google Scholar 

  60. Wang, G.Y., Li, T., Ai, Q., Alsaedi, A., Hayat, T., Deng, F.G., et al.: Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems. Phys. Rev. Appl. 10(5), 054058 (2018)

    Article  ADS  Google Scholar 

  61. Wang, G.Y., Ai, Q., Deng, F.G., Ren, B.C.: Imperfect-interaction-free entanglement purification on stationary systems for solid quantum repeaters. Opt. Express 28(13), 18693 (2020)

    Article  ADS  Google Scholar 

  62. Lu, L.C., Ren, B.C., Wang, X., Zhang, M., Deng, F.G.: General quantum entanglement purification protocol using a controlled-phase-flip gate. Ann. Phys. 532(4), 2000011 (2020)

    Article  MathSciNet  Google Scholar 

  63. Wang, C.: Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system. Phys. Rev. A 86(1), 012323 (2012)

    Article  ADS  Google Scholar 

  64. Sheng, Y.B., Zhou, L., Wang, L., Zhao, S.M.: Efficient entanglement concentration for quantum dot and optical microcavities systems. Quantum Inf. Process. 12(5), 1885 (2013)

    Article  ADS  MATH  Google Scholar 

  65. Du, F.F., Long, G.L.: Refined entanglement concentration for electron-spin entangled cluster states with quantum-dot spins in optical microcavities. Quantum Inf. Process. 16(1), 26 (2017)

    Article  ADS  MATH  Google Scholar 

  66. Liu, A.P., Cheng, L.Y., Guo, Q., Su, S.L., Wang, H.F., Zhang, S.: Heralded entanglement concentration of nonlocal photons assisted by doublesided optical microcavities. Phys. Scr. 94(9), 095103 (2019)

    Article  ADS  Google Scholar 

  67. Warburton, R., Dürr, C., Karrai, K., Kotthaus, J., Medeiros-Ribeiro, G., Petroff, P.: Charged excitons in self-assembled semiconductor quantum dots. Phys. Rev. Lett. 79(26), 5282 (1997)

    Article  ADS  Google Scholar 

  68. Panzarini, G., Andreani, L.C., Armitage, A., Baxter, D., Skolnick, M., Astratov, V., Roberts, J., Kavokin, A.V., Vladimirova, M.R., Kaliteevski, M.: Cavity-polariton dispersion and polarization splitting in single and coupled semiconductor microcavities. Phys. Solid State 41(8), 1223 (1999)

    Article  ADS  Google Scholar 

  69. Langbein, W., Borri, P., Woggon, U., Stavarache, V., Reuter, D., Wieck, A.: Control of fine-structure splitting and biexciton binding in quantum dots by annealing. Phys. Rev. B 69(16), 161301 (2004)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61701035 and 61671085 and by Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), P. R. China.

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Correspondence to Cong Cao.

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Yin, PP., Cao, C., Han, YH. et al. Faithful quantum entanglement purification and concentration using heralded high-fidelity parity-check detectors based on quantum-dot-microcavity systems. Quantum Inf Process 21, 17 (2022). https://doi.org/10.1007/s11128-021-03371-y

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