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Quantum tele-amplification with a continuous-variable superposition state


Optical coherent states are classical light fields with high purity, and are essential carriers of information in optical networks. If these states could be controlled in the quantum regime, allowing for their quantum superposition (referred to as a Schrödinger-cat state), then novel quantum-enhanced functions such as coherent-state quantum computing (CSQC)1,2,3,4,5, quantum metrology6,7 and a quantum repeater8,9 could be realized in the networks. Optical cat states are now routinely generated in laboratories. An important next challenge is to use them for implementing the aforementioned functions. Here, we demonstrate a basic CSQC protocol, where a cat state is used as an entanglement resource for teleporting a coherent state with an amplitude gain. We also show how this can be extended to a loss-tolerant quantum relay of multi-ary phase-shift keyed coherent states. These protocols could be useful in both optical and quantum communications.

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Figure 1: Scheme of quantum tele-amplification and quantum relay.
Figure 2: Measured results for 12 cases.
Figure 3: Simulated average qubit teleportation fidelity.


  1. Cochrane, P. T., Milburn, G. J. & Munro, W. J. Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping. Phys. Rev. A 59, 2631–2634 (1999).

    Article  ADS  Google Scholar 

  2. Jeong, H. & Kim, M. S. Efficient quantum computation using coherent states. Phys. Rev. A 65, 042305 (2002).

    Article  ADS  Google Scholar 

  3. Ralph, T. C., Gilchrist, A., Milburn, G., Munro, W. J. & Glancy, S. Quantum computation with optical coherent states. Phys. Rev. A 68, 042319 (2003).

    Article  ADS  Google Scholar 

  4. Jeong, H. & Ralph, T. C. in Quantum Information with Continuous Variables of Atoms and Light (eds Cerf, N. J., Leuchs G. & Polzik, E. S.) Ch. 9 (Imperial College Press, 2007).

    Google Scholar 

  5. Lund, A. P., Ralph, T. C. & Haselgrove, H. L. Fault-tolerant linear optical quantum computing with small-amplitude coherent states. Phys. Rev. Lett. 100, 030503 (2008).

    Article  ADS  Google Scholar 

  6. Gerry, C., Benmoussa, A. & Campos, R. Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry. Phys. Rev. A 66, 013804 (2002).

    Article  ADS  Google Scholar 

  7. Joo, J., Munro, W. J. & Spiller, T. Quantum metrology with entangled coherent states. Phys. Rev. Lett. 107, 083601 (2011).

    Article  ADS  Google Scholar 

  8. Sangouard, N. et al. Quantum repeaters with entangled coherent states. J. Opt. Soc. Am. B 27, A137–A145 (2010).

    Article  Google Scholar 

  9. Brask, J. B. et al. Hybrid long-distance entanglement distribution protocol. Phys. Rev. Lett. 105, 160501 (2010).

    Article  ADS  Google Scholar 

  10. Giovannetti, V. et al. Classical capacity of the lossy bosonic channel: the exact solution. Phys. Rev. Lett. 92, 027902 (2004).

    Article  ADS  Google Scholar 

  11. Sasaki, M., Sasaki-Usuda, T., Izutsu, M. & Hirota, O. Realization of a collective decoding of code-word states. Phys. Rev. A 58, 159–164 (1998).

    Article  ADS  Google Scholar 

  12. Waseda, A., Takeoka, M., Sasaki, M., Fujiwara, M. & Tanaka, H. Quantum detection of wavelength-division-multiplexing optical coherent signals. J. Opt. Soc. Am. B 27, 259–265 (2010).

    Article  ADS  Google Scholar 

  13. Ourjoumtsev, A., Tualle-Brouri, R., Laurat, J. & Grangier, P. Generating optical Schrödinger kittens for quantum information processing. Science 312, 83–86 (2006).

    Article  ADS  Google Scholar 

  14. Neergaard-Nielsen, J. S., Nielsen, B. M., Hettich, C., Mølmer, K. & Polzik, E. S. Generation of a superposition of odd photon number states for quantum information networks. Phys. Rev. Lett. 97, 083604 (2006).

    Article  ADS  Google Scholar 

  15. Wakui, K., Takahashi, H., Furusawa, A. & Sasaki, M. Photon subtracted squeezed states generated with periodically poled KTiOPO4 . Opt. Express 15, 3568–3574 (2007).

    Article  ADS  Google Scholar 

  16. Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R. & Grangier, P. Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784–786 (2007).

    Article  ADS  Google Scholar 

  17. Takahashi, H. et al. Generation of large-amplitude coherent-state superposition via ancilla-assisted photon subtraction. Phys. Rev. Lett. 101, 233605 (2008).

    Article  ADS  Google Scholar 

  18. Neergaard-Nielsen, J. S. et al. Optical continuous-variable qubit. Phys. Rev. Lett. 105, 053602 (2010).

    Article  ADS  Google Scholar 

  19. Lee, N. et al. Teleportation of nonclassical wave packets of light. Science 332, 330–333 (2011).

    Article  ADS  Google Scholar 

  20. Van Enk, S. J. & Hirota, O. Entangled coherent states: teleportation and decoherence. Phys. Rev. A 64, 022313 (2001).

    Article  ADS  Google Scholar 

  21. Jeong, H., Kim, M. & Lee, J. Quantum-information processing for a coherent superposition state via a mixed entangled coherent channel. Phys. Rev. A 64, 052308 (2001).

    Article  ADS  Google Scholar 

  22. Jacobs, B., Pittman, T. & Franson, J. Quantum relays and noise suppression using linear optics. Phys. Rev. A 66, 052307 (2002).

    Article  ADS  Google Scholar 

  23. Collins, D., Gisin, N. & De Riedmatten, H. Quantum relays for long distance quantum cryptography. J. Mod. Opt. 52, 735–753 (2005).

    Article  ADS  Google Scholar 

  24. Koashi, M. Unconditional security of coherent-state quantum key distribution with a strong phase-reference pulse. Phys. Rev. Lett. 93, 120501 (2004).

    Article  ADS  Google Scholar 

  25. Tamaki, K., Lütkenhaus, N., Koashi, M. & Batuwantudawe, J. Unconditional security of the Bennett 1992 quantum-key-distribution scheme with a strong reference pulse. Phys. Rev. A 80, 032302 (2009).

    Article  ADS  Google Scholar 

  26. Lo, H-K. & Preskill, J. Security of quantum key distribution using weak coherent states with nonrandom phases. Quant. Inf. Comp. 7, 431–458 (2007).

    MathSciNet  MATH  Google Scholar 

  27. Takeoka, M. et al. Engineering of optical continuous-variable qubits via displaced photon subtraction: multimode analysis. J. Mod. Opt. 58, 266–275 (2011).

    Article  ADS  Google Scholar 

  28. Xiang, G. Y., Ralph, T. C., Lund, A. P., Walk, N. & Pryde, G. J. Heralded noiseless linear amplification and distillation of entanglement. Nature Photon. 4, 316–319 (2010).

    Article  Google Scholar 

  29. Zavatta, A., Fiurášek, J. & Bellini, M. A high-fidelity noiseless amplifier for quantum light states. Nature Photon. 5, 52–60 (2010).

    Article  ADS  Google Scholar 

  30. Ferreyrol, F., Blandino, R., Barbieri, M., Tualle-Brouri, R. & Grangier, P. Experimental realization of a nondeterministic optical noiseless amplifier. Phys. Rev. A 83, 063801 (2011).

    Article  ADS  Google Scholar 

  31. Brańczyk, A. & Ralph, T. C. Teleportation using squeezed single photons. Phys. Rev. A 78, 052304 (2008).

    Article  ADS  Google Scholar 

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The authors acknowledge helpful discussions with K. Wakui, M. Takeoka, K. Hayasaka, M. Fujiwara, T.C. Ralph, A.P. Lund, K. Tamaki and M. Koashi. This work was partly supported by the Quantum Information Processing Project in the Program for World-Leading Innovation Research and Development on Science and Technology (FIRST) and by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (Ministry of Education, Science, and Technology; no. 2010-0018295).

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Authors and Affiliations



M.S. and J.S.N-N. formulated the basic protocol of tele-amplification and loss-tolerant quantum relay, inspired by a teleportation scheme by C-W.L. and H.J. J.S.N-N. and Y.E. carried out the experiment. J.S.N-N., C-W.L., M.S. and H.J. performed the theoretical calculations. J.S.N-N. and M.S. wrote the manuscript, with discussions and input from all authors.

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Correspondence to Masahide Sasaki.

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The authors declare no competing financial interests.

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Neergaard-Nielsen, J., Eto, Y., Lee, CW. et al. Quantum tele-amplification with a continuous-variable superposition state. Nature Photon 7, 439–443 (2013).

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