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Continuous-variable quantum network coding for coherent states

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Abstract

As far as the spectral characteristic of quantum information is concerned, the existing quantum network coding schemes can be looked on as the discrete-variable quantum network coding schemes. Considering the practical advantage of continuous variables, in this paper, we explore two feasible continuous-variable quantum network coding (CVQNC) schemes. Basic operations and CVQNC schemes are both provided. The first scheme is based on Gaussian cloning and ADD/SUB operators and can transmit two coherent states across with a fidelity of 1/2, while the second scheme utilizes continuous-variable quantum teleportation and can transmit two coherent states perfectly. By encoding classical information on quantum states, quantum network coding schemes can be utilized to transmit classical information. Scheme analysis shows that compared with the discrete-variable paradigms, the proposed CVQNC schemes provide better network throughput from the viewpoint of classical information transmission. By modulating the amplitude and phase quadratures of coherent states with classical characters, the first scheme and the second scheme can transmit \(4{\log _2}N\) and \(2{\log _2}N\) bits of information by a single network use, respectively.

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References

  1. Ahlswede, R., Cai, N., Li, S.Y.R., et al.: Network information flow. IEEE Trans. Inf. Theory 46(4), 1204–1216 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hayashi, M., Iwama, K.: Quantum network coding. In: Proceedings of the 2007 Symposium 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 76(4), 1–5 (2007)

    Article  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. Braunstein, S.L., Loock, P.V.: Quantum information with continuous variables. Rev. Mod. Phys. 77(2), 513–577 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Vaidman, L.: Teleportation of quantum states. Phys. Rev. A 49(2), 1473–1476 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  7. Hillery, M.: Quantum cryptography with squeezed states. Phys. Rev. A 61(2), 022309 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  8. Cerf, N.J., Lvy, M., Assche, G.V.: Quantum distribution of Gaussian keys using squeezed states. Phys. Rev. A 63(5), 535–540 (2001)

    Article  Google Scholar 

  9. Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88(5), 057902 (2002)

  10. Bartlett, S.D., Sanders, B.C., Braunstein, S.L., et al.: Efficient classical simulation of continuous variable quantum information processes. Phys. Rev. Lett. 88(9), 47–55 (2001)

    Google Scholar 

  11. Miwa, Y., Yoshikawa, J.I., van Loock, P., et al.: Demonstration of a universal one-way quantum quadratic phase gate. Phys. Rev. A 80(5), 050303 (2009)

    Article  ADS  Google Scholar 

  12. Cerf, N.J., Ipe, A., Rottenberg, X.: Cloning of continuous quantum variables. Phys. Rev. Lett. 85(8), 1754–1757 (2000)

    Article  ADS  Google Scholar 

  13. Fiurasek, J.: Optical implementation of continuous-variable quantum cloning machines. Phys. Rev. Lett. 86(21), 4942 (2001)

    Article  ADS  Google Scholar 

  14. Andersen, U.L., Josse, V., Leuchs, G.: Unconditional quantum cloning of coherent states with linear optics. Phys. Rev. Lett. 94(24), 240503 (2005)

    Article  ADS  Google Scholar 

  15. Zeng, G., Lee, M., Guo, Y., et al.: Continuous variable quantum signature algorithm. Int. Quantum Inf. 5(4), 553–573 (2007)

    Article  MATH  Google Scholar 

  16. Weedbrook, C., Lance, A.M., Bowen, W.P., et al.: Quantum cryptography without switching. Phys. Rev. Lett. 93(17), 170504-1–170504-4 (2004)

    Article  ADS  Google Scholar 

  17. Zavatta, A., Fiurasek, J., Bellini, M.: A high-fidelity noiseless amplifier for quantum light states. Nat. Photonics 5(1), 52–60 (2011)

    Article  ADS  Google Scholar 

  18. Grosshans, F., Grangier, P.: Quantum cloning and teleportation criteria for continuous quantum variables. Phys. Rev. A 64(1), 783–97 (2001)

    Article  MathSciNet  Google Scholar 

  19. Bernstein, H.J.: Must quantum theory assume unrestricted superposition? J. Math. Phys. 15(10), 1677–1679 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  20. Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80(4), 869 (1998)

    Article  ADS  Google Scholar 

  21. Braunstein, S.L., Fuchs, C.A., Kimble, H.J.: Criteria for continuous-variable quantum teleportation. J. Mod. Opt. 47(2–3), 267–278 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  22. Banaszek, K.: Optimal receiver for quantum cryptography with two coherent states. Phys. Lett. A 253(1), 12–15 (1999)

    Article  ADS  Google Scholar 

  23. van Enk, S.J.: Unambiguous state discrimination of coherent states with linear optics: application to quantum cryptography. Phys. Rev. A 66, 042313 (2002)

    Article  ADS  Google Scholar 

  24. Muller, C., Usuga, M.A., Wittmann, C., et al.: Quadrature phase shift keying coherent state discrimination via a hybrid receiver. New J. Phys. 14(8), 83009–83021 (2012)

    Article  Google Scholar 

  25. Becerra, F.E., Fan, J., Migdall, A.: Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states. Nat. Commun. 4(3), 131–140 (2013)

    Google Scholar 

  26. da Silva, M.P., Guha, S., Dutton, Z.: Optimal discrimination of M coherent states with a small quantum computer. In: Eleventh International Conference on Quantum Communication, Measurement and Computation (QCMC), vol. 1633(1), pp. 225–227 (2014)

  27. Gottesman, D., Kitaev, A., Preskill, J.: Encoding a qubit in an oscillator. Phys. Rev. A 64(1), 012310 (2001)

    Article  ADS  Google Scholar 

  28. Chuang, I.L., Leung, D.W., Yamamoto, Y.: Bosonic quantum codes for amplitude damping. Phys. Rev. A 56(2), 1114 (1997)

    Article  ADS  Google Scholar 

  29. Holevo, A.S., Werner, R.F.: Evaluating capacities of bosonic Gaussian channels. Phys. Rev. A 63(3), 032312 (2001)

    Article  ADS  Google Scholar 

  30. Holevo, A.S.: One-mode quantum Gaussian channels: structure and quantum capacity. Probl. Inf. Transm. 43(1), 1–11 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  31. Weedbrook, C., Pirandola, S., Garca-Patrn, R., et al.: Gaussian quantum information. Rev. Mod. Phys. 84(2), 621 (2012)

    Article  ADS  Google Scholar 

  32. Caruso, F., Giovannetti, V.: Degradability of bosonic Gaussian channels. Phys. Rev. A 74(6), 062307 (2006)

    Article  ADS  Google Scholar 

  33. Cubitt, T., Elkouss, D., Matthews, W., et al.: Unbounded number of channel uses may be required to detect quantum capacity. Nat. Commun. 6, 6739 (2015)

    Article  ADS  Google Scholar 

  34. Caves, C.M.: Quantum limits on noise in linear amplifiers. Phys. Rev. D 26(8), 1817 (1982)

    Article  ADS  Google Scholar 

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Acknowledgements

This project was supported by the National Natural Science Foundation of China (No. 61571024) and the National Key Research and Development Program of China (No. 2016YFC1000307) for valuable helps.

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Beihang University, Beijing, 100083, China

    Tao Shang, Ke Li & Jian-wei Liu

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  1. Tao Shang
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  2. Ke Li
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  3. Jian-wei Liu
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Correspondence to Tao Shang.

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Shang, T., Li, K. & Liu, Jw. Continuous-variable quantum network coding for coherent states. Quantum Inf Process 16, 107 (2017). https://doi.org/10.1007/s11128-017-1565-3

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