Efficient quantum state transmission via perfect quantum network coding

Abstract

Quantum network coding with the assistance of auxiliary resources can achieve perfect transmission of the quantum state. This paper suggests a novel perfect network coding scheme to efficiently solve the quantum k-pair problem, in which only a few assisting resources are introduced. Specifically, only one pair of maximally entangled state needs to be pre-shared between two intermediate nodes, and only O(k) of classical information is transmitted though the network. Moreover, the classical communication used in our protocol does not cause transmission congestion, providing better adaptability to large-scale quantum k-pair networks. Through relevant analyses and comparisons, we demonstrate that our proposed scheme saves resources and has good application value, thereby showing its high efficiency. Furthermore, the proposed scheme achieves 1-max flow quantum communication, and the achievable rate region result is extended from its counterpart over the butterfly network.

This is a preview of subscription content, access via your institution.

References

  1. 1

    Ahlswede R, Cai N, Li S Y R, et al. Network information flow. IEEE Trans Inform Theor, 2000, 46: 1204–1216

    MathSciNet  MATH  Google Scholar 

  2. 2

    Li S Y R, Yeung R W, Cai N. Linear network coding. IEEE Trans Inform Theor, 2003, 49: 371–381

    MathSciNet  MATH  Google Scholar 

  3. 3

    Ding L H, Wu P, Wang H, et al. Lifetime maximization routing with network coding in wireless multihop networks. Sci China Inf Sci, 2013, 56: 022303

    MathSciNet  Google Scholar 

  4. 4

    Zhang C S, Ge J H, Li J, et al. Robust power allocation algorithm for analog network coding with imperfect CSI. Sci China Inf Sci, 2014, 57: 042312

    Google Scholar 

  5. 5

    Guo R N, Zhang Z Y, Liu X P, et al. Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays. Appl Math Comput, 2017, 311: 100–117

    MathSciNet  MATH  Google Scholar 

  6. 6

    Pang Z, Liu G, Zhou D, et al. Data-based predictive control for networked nonlinear systems with packet dropout and measurement noise. J Syst Sci Complex, 2017, 30: 1072–1083

    MathSciNet  MATH  Google Scholar 

  7. 7

    Li L, Wang Z, Li Y, et al. Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays. Appl Math Comput, 2018, 330: 152–169

    MathSciNet  MATH  Google Scholar 

  8. 8

    Shen H, Song X, Li F, et al. Finite-time L2L filter design for networked Markov switched singular systems: a unified method. Appl Math Comput, 2018, 321: 450–462

    MathSciNet  Google Scholar 

  9. 9

    Shin W Y, Chung S Y, Lee Y H. Parallel opportunistic routing in wireless networks. IEEE Trans Inform Theor, 2013, 59: 6290–6300

    MathSciNet  MATH  Google Scholar 

  10. 10

    Bell J S. On the Einstein Podolsky Rosen paradox. Phys Physique Fizika, 1964, 1: 195–200

    MathSciNet  Google Scholar 

  11. 11

    Gisin N. Bell’s inequality holds for all non-product states. Phys Lett A, 1991, 154: 201–202

    MathSciNet  Google Scholar 

  12. 12

    Popescu S, Rohrlich D. Generic quantum nonlocality. Phys Lett A, 1992, 166: 293–297

    MathSciNet  Google Scholar 

  13. 13

    Dong H, Zhang Y, Zhang Y, et al. Generalized bilinear differential operators, binary bell polynomials, and exact periodic wave solution of boiti-leon-manna-pempinelli equation. In: Proceedings of Abstract and Applied Analysis, Hindawi, 2014

    Google Scholar 

  14. 14

    Jiang T, Jiang Z, Ling S. An algebraic method for quaternion and complex least squares coneigen-problem in quantum mechanics. Appl Math Comput, 2014, 249: 222–228

    MathSciNet  MATH  Google Scholar 

  15. 15

    Chaves R. Polynomial bell inequalities. Phys Rev Lett, 2016, 116: 010402

    MathSciNet  MATH  Google Scholar 

  16. 16

    Rosset D, Branciard C, Barnea T J, et al. Nonlinear bell inequalities tailored for quantum networks. Phys Rev Lett, 2016, 116: 010403

    MathSciNet  MATH  Google Scholar 

  17. 17

    Gisin N, Mei Q, Tavakoli A, et al. All entangled pure quantum states violate the bilocality inequality. Phys Rev A, 2017, 96: 020304

    MathSciNet  Google Scholar 

  18. 18

    Luo M X. Computationally efficient nonlinear bell inequalities for quantum networks. Phys Rev Lett, 2018, 120: 140402

    MathSciNet  Google Scholar 

  19. 19

    Hu M J, Zhou Z Y, Hu X M, et al. Experimental sharing of nonlocality among multiple observers with one entangled pair via optimal weak measurements. 2016. ArXiv: 1609.01863

    Google Scholar 

  20. 20

    Hayashi M, Iwama K, Nishimura H. Quantum network coding. In: Proceedings of the 24th Annual Conference on Theoretical Aspects of Computer Science. Berlin: Springer, 2007. 610–621

    Google Scholar 

  21. 21

    Tang X H, Li Z P, Wu C, et al. A geometric perspective to multiple-unicast network coding. IEEE Trans Inform Theor, 2014, 60: 2884–2895

    MathSciNet  MATH  Google Scholar 

  22. 22

    Harvey N J, Kleinberg R D, Lehman A R. Comparing Network Coding with Multicommodity Flow for the k-pairs Communication Problem. MIT LCS Technical Report 964. 2004

    Google Scholar 

  23. 23

    Dougherty R, Zeger K. Nonreversibility and equivalent constructions of multiple-unicast networks. IEEE Trans Inform Theor, 2006, 52: 5067–5077

    MathSciNet  MATH  Google Scholar 

  24. 24

    Curty M, Lewenstein M, Lütkenhaus N. Entanglement as a precondition for secure quantum key distribution. Phys Rev Lett, 2004, 92: 217903

    Google Scholar 

  25. 25

    Ren X. Quantum correlations generation and distribution in a universal covariant quantum cloning circuit. Sci China Inf Sci, 2017, 60: 122501

    Google Scholar 

  26. 26

    Bennett C H, Brassard G, Crépeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1993, 70: 1895–1899

    MathSciNet  MATH  Google Scholar 

  27. 27

    Chen X B, Su Y, Xu G, et al. Quantum state secure transmission in network communications. Inf Sci, 2014, 276: 363–376

    MathSciNet  MATH  Google Scholar 

  28. 28

    Dou Z, Xu G, Chen X B, et al. A secure rational quantum state sharing protocol. Sci China Inf Sci, 2018, 61: 022501

    MathSciNet  Google Scholar 

  29. 29

    Hayashi M. Prior entanglement between senders enables perfect quantum network coding with modification. Phys Rev A, 2007, 76: 040301

    MathSciNet  Google Scholar 

  30. 30

    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, 2010, 283: 497–501

    Google Scholar 

  31. 31

    Satoh T, Le Gall F, Imai H. Quantum network coding for quantum repeaters. Phys Rev A, 2012, 86: 032331

    Google Scholar 

  32. 32

    Satoh T, Ishizaki K, Nagayama S, et al. Analysis of quantum network coding for realistic repeater networks. Phys Rev A, 2016, 93: 032302

    Google Scholar 

  33. 33

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

    MathSciNet  MATH  Google Scholar 

  34. 34

    Mahdian M, Bayramzadeh R. Perfect k-pair quantum network coding using superconducting qubits. J Supercond Nov Magn, 2015, 28: 345–348

    Google Scholar 

  35. 35

    Li J, Chen X B, Sun X M, et al. Quantum network coding for multi-unicast problem based on 2D and 3D cluster states. Sci China Inf Sci, 2016, 59: 042301

    Google Scholar 

  36. 36

    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, 2018, 61: 060312

    Google Scholar 

  37. 37

    Shang T, Li K, Liu J. Continuous-variable quantum network coding for coherent states. Quantum Inf Process, 2017, 16: 107

    MathSciNet  MATH  Google Scholar 

  38. 38

    Nguyen H V, Babar Z, Alanis D, et al. Towards the quantum Internet: generalised quantum network coding for large-scale quantum communication networks. IEEE Access, 2017, 5: 17288–17308

    Google Scholar 

  39. 39

    Li D D, Gao F, Qin S J, et al. Perfect quantum multiple-unicast network coding protocol. Quantum Inf Process, 2018, 17: 13

    MathSciNet  MATH  Google Scholar 

  40. 40

    Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. 10th ed. New York: Cambridge University Press, 2010

    Google Scholar 

  41. 41

    Kobayashi H, Le Gall F, Nishimura H, et al. General scheme for perfect quantum network coding with free classical communication. In: Proceedings of the 36th International Colloquium on Automata, Languages and Programming, Greece, 2009. 622–633

    Google Scholar 

  42. 42

    Kobayashi H, Le Gall F, Nishimura H, et al. Constructing quantum network coding schemes from classical nonlinear protocols. In: Proceedings of the IEEE Int Symp Information Theory (ISIT), New York, 2011. 109–113

    Google Scholar 

  43. 43

    Li J, Chen X B, Xu G, et al. Perfect quantum network coding independent of classical network solutions. IEEE Commun Lett, 2015, 19: 115–118

    Google Scholar 

  44. 44

    Yang Y, Yang J, Zhou Y, et al. Quantum network communication: a discrete-time quantum-walk approach. Sci China Inf Sci, 2018, 61: 042501

    MathSciNet  Google Scholar 

  45. 45

    de Beaudrap N, Roetteler M. Quantum linear network coding as one-way quantum computation. 2014. ArXiv: 1403.3533

    Google Scholar 

  46. 46

    Kobayashi H, Le Gall F, Nishimura H, et al. Perfect quantum network communication protocol based on classical network coding. In: Proceedings of the IEEE Int Symp Information Theory, New York, 2010. 2686–2690

    Google Scholar 

  47. 47

    Leung D, Oppenheim J, Winter A. Quantum network communication-the butterfly and beyond. IEEE Trans Inform Theor, 2010, 56: 3478–3490

    MathSciNet  MATH  Google Scholar 

  48. 48

    Nishimura H. Quantum network coding–how can network coding be applied to quantum information? In: Proceedings of the 2013 IEEE International Symposium on Network Coding, 2013. 1–5

    Google Scholar 

  49. 49

    Jain A, Franceschetti M, Meyer D A. On quantum network coding. J Math Phys, 2011, 52: 032201

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61671087, 61272514, 61170272, 61003287, 61373131), the Fok Ying Tong Education Foundation (Grant No. 131067), and the Major Science and Technology Support Program of Guizhou Province (Grant No. 20183001).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Gang Xu.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, ZZ., Xu, G., Chen, XB. et al. Efficient quantum state transmission via perfect quantum network coding. Sci. China Inf. Sci. 62, 12501 (2019). https://doi.org/10.1007/s11432-018-9592-9

Download citation

Keywords

  • perfect quantum network coding
  • quantum k-pair problem
  • efficient quantum state transmission
  • communication efficiency
  • achievable rate region