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Quantum network coding reducing decoherence effect

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Abstract

Quantum decoherence leads to environment-induced superselection of preferred states. Some information in the measurement apparatus is lost during communication. Even if the measurement apparatus is not entangled with the system of interest, the loss of information would occur. In this paper, we propose a feasible quantum network coding scheme reducing decoherence effect to transmit the mutual information between source node and target node. With the help of entanglement distribution by separable states, the quantum network coding scheme initially achieves quantum entanglement distribution of two crossing source-target pairs in a butterfly network. Furthermore, by means of transmission of correlations, the maximal mutual information resulting from local operations and classical communication will be transmitted to a distant receiver. Compared with the representative quantum network coding schemes, the proposed scheme transmits correlations rather than quantum state over the butterfly network. The upper bound to the concentrated information is also quantified. Analysis indicates that the proposed scheme can effectively defend against active attacks with fewer resource consumption and good region rate.

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References

  1. Shang, T., Liu, J.W.: Secure Quantum Network Coding Theory. Springer, Berlin (2020)

    Book  Google Scholar 

  2. Hayashi, M., Iwamam, K.: Quantum network coding. Theoretical Aspects of Computer Science. Lecture Notes in Computer Science. vol. 4393, pp. 610–621 (2007)

  3. Hayashi, M.: Prior entanglement between senders enables perfect quantum network coding with modification. Phys. Rev. A vol 76(4), 538 (2007)

    MathSciNet  Google Scholar 

  4. Satoh, T., Gall, F.L., Imai, H.: Quantum network coding for quantum repeaters. Phys. Rev. A 86(3), 1–8 (2012)

    Article  Google Scholar 

  5. Shang, T., Li, K., Liu, J.W.: Continuous-variable quantum network coding for coherent states. Quantum Inf. Process. vol 20(4), 291 (2017)

    MathSciNet  MATH  Google Scholar 

  6. Bennett, C.H., Divincenzo, D.P.: Quantum information and computation. Nature 48(10), 24–30 (1995)

    Google Scholar 

  7. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88(1), 017901 (2001)

    Article  ADS  Google Scholar 

  8. Zurek, W.H.: Quantum discord and Maxwell’s demons. Physics 67(1), 012320 (2003)

  9. Streltsov, A., Kampermann, H., Bruss, D.: Linking quantum discord to entanglement in a measurement. Phys. Rev. Lett. vol 106(16), 160401.1-160401.4 (2011)

    ADS  Google Scholar 

  10. Madhok, V., Datta, A.: Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323 (2011)

    Article  ADS  Google Scholar 

  11. Zurek, W.H.: Quantum Darwinism, classical reality, and the randomness of quantum jumps. Phys. Today 67(10), 44–50 (2014)

    Article  Google Scholar 

  12. Zurek, W.H.: Decoherence, einselection and the quantum origins of the classical. Rev. Mod. Phys. 75(3), 715–775 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  13. Modi, K., Brodutch, A.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  14. Streltsov, A., Zurek, W.H.: Quantum discord cannot be shared. Phys. Rev. Lett. vol 111(4), 040401.1-040401.5 (2013)

    ADS  Google Scholar 

  15. Bohr, N.: Essays on atomic physics and human knowledge. Philos. Phenomenol. Res. vol 21(8), 276 (1960)

    Google Scholar 

  16. Chitambar, E., Duan, R., Hsieh, M.H.: When do local operations and classical communication suffice for two-qubit state discrimination? IEEE Trans. Inf. Theory 60(3), 1549–1561 (2014)

    Article  MathSciNet  Google Scholar 

  17. Zurek, W.H.: Quantum darwinism. Nat. Phys. 5, 181–188 (2009)

    Article  Google Scholar 

  18. Horodecki, R., Korbicz, J.K., Horodecki, P.: Quantum origins of objectivity. Phys. Rev. A 91(3), 032122 (2015)

    Article  ADS  Google Scholar 

  19. Ollivier, H., Poulin, D., Zurek, W.H.: Objective properties from subjective quantum states: environment as a witness. Phys. Rev. Lett. vol 93(22), 220401.1-220401.4 (2004)

    ADS  Google Scholar 

  20. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Gen. Phys. 34(35), 6899–6905 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  21. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88(1), 017901 (2002)

    Article  ADS  Google Scholar 

  22. Streltsov, A., Lee, S., Adesso, G.: Concentrating tripartite quantum information. Phys. Rev. Lett 115(3), 030505 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  23. Devetak, I., Winter, A.: Distillation of secret key and entanglement from quantum states. Proc. R. Soc. A: Math. Phys. Eng. Sci. 461, 207–235 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  24. Leung, D., Oppenheim, J., Winter, A.: Quantum network communication—the butterfly and beyond. IEEE Trans. Inf. Theory 56, 3478–3490 (2010)

    Article  MathSciNet  Google Scholar 

  25. Bru, D., Divincenzo, D.P., Ekert, A., et al.: Optimal universal and state-dependent quantum cloning. Phys. Rev. A 57(4), 2368–2378 (1997)

    ADS  Google Scholar 

  26. Ma, S.Y., Chen, X.B., Luo, M.X., et al.: Probabilistic quantum network coding of M-qudit states over the butterfly network. Opt. Commun. 283(3), 497–501 (2010)

    Article  ADS  Google Scholar 

  27. Zhang, S., Li, J., Dong, H.J., et al.: Quantum network coding on networks with arbitrarily distributed hidden channels. Commun. Theor. Phys. 60(10), 415–420 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  28. Wang, F., Luo, M.X., Xu, G., et al.: Photonic quantum network transmission assisted by the weak cross-kerr nonlinearity. Sci. China Phys. Mech. Astron. 61(6), 8–23 (2018)

    Article  ADS  Google Scholar 

  29. Bennett, C.H., Brassard, G., Popescu, S., et al.: Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels. Phys. Rev. Lett. 76(5), 722–725 (1996)

    Article  ADS  Google Scholar 

  30. 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 

  31. Borregaard, J., Komar, P., Kessler, E.M., et al.: Long-distance entanglement distribution using individual atoms in optical cavities. Phys. Rev. A 92(1), 012307 (2015)

    Article  ADS  Google Scholar 

  32. Zhang, C.W., Li, C.F., Wang, Z.Y., Guo, G.C.: Probabilistic quantum cloning via Greenberger–Horne–Zeilinger states. Phys. Rev. A 62(4), 190–191 (2000)

    Article  MathSciNet  Google Scholar 

  33. Galve, F., Zambrini, R., Maniscalco, S.: Non-Markovianity hinders quantum Darwinism. Sci. Rep. 6, 19607 (2016)

    Article  ADS  Google Scholar 

  34. Reiserer, A., Rempe, G.: Cavity-based quantum networks with single atoms and optical photons. Rev. Mod. Phys. vol 87(4), 1379 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This project was supported by the National Natural Science Foundation of China (No. 61971021 and 61571024), the Aeronautical Science Foundation of China (No. 2018ZC51016) and the National Key Research and Development Program of China (No. 2016YFC1000307).

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Authors and Affiliations

  1. School of Cyber Science and Technology, Beihang University, Beijing, 100083, China

    Tao Shang, Yuanjing Zhang, Ran Liu & Jianwei Liu

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  1. Tao Shang
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  2. Yuanjing Zhang
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  3. Ran Liu
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  4. Jianwei Liu
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Correspondence to Tao Shang.

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Shang, T., Zhang, Y., Liu, R. et al. Quantum network coding reducing decoherence effect. Quantum Inf Process 20, 267 (2021). https://doi.org/10.1007/s11128-021-03200-2

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