Abstract

We propose a teleportation scheme for nondestructively transmitting an unknown qudit state between two remote communication parties that are linked by sequential Bell pairs. With independent and simultaneous entanglement swapping among the intermediate nodes, a direct entangled channel between the source node and the destination node is established. Our scheme preserves the initial unknown state even if the teleportation fails. Different nonmaximally entangled channels are distributed among the participants so that the quantum channel requirement is reduced. In addition, the communication delay is reduced significantly since the measuring and the transmitting are conducted simultaneously by the intermediate nodes.

© 2020 Optical Society of America

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References

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    [Crossref]
  2. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eib, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
    [Crossref]
  3. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
    [Crossref]
  4. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum mechanical description of physical reality be considered complete,” Phys. Rev. 48, 777–780 (1935).
    [Crossref]
  5. D. Boschi, S. Branca, F. D. Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (2010).
    [Crossref]
  6. T. J. Wang, H. Y. Zhou, and F. G. Deng, “Quantum state sharing of an arbitrary m-qudit state with two-qudit entanglements and generalized Bell-state measurements,” Phys. A 387, 4716–4722 (2008).
    [Crossref]
  7. E. O. Kiktenko, A. A. Popov, and A. K. Fedorov, “Bidirectional imperfect quantum teleportation with a single Bell state,” Phys. Rev. A 93, 062305 (2016).
    [Crossref]
  8. Z. J. Zhang, “Controlled teleportation of an arbitrary n-qubit quantum information using quantum secret sharing of classical message,” Phys. Lett. A 352, 55–58 (2006).
    [Crossref]
  9. Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyper-entangled Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
    [Crossref]
  10. Y. B. Sheng and L. Zhou, “Entanglement analysis for macroscopic Schrödinger’s Cat state,” Europhys. Lett. 109, 40009 (2015).
    [Crossref]
  11. F. L. Yan and D. Wang, “Probabilistic and controlled teleportation of unknown quantum states,” Phys. Lett. A 316, 297–303 (2003).
    [Crossref]
  12. F. L. Yan and T. Yan, “Probabilistic teleportation via a non-maximally entangled GHZ state,” Chin. Sci. Bull. 55, 902–906 (2009).
    [Crossref]
  13. L. Zhou and Y. B. Sheng, “Feasible logic Bell-state analysis with linear optics,” Sci. Rep. 6, 20901 (2016).
    [Crossref]
  14. J. Dong and J. F. Teng, “Probabilistic controlled teleportation of a triplet W state with combined channel of non-maximally entangled Einstein–Podolsky–Rosen and Greenberger–Horne–Zeilinger states,” Chin. Phys. Lett. 26, 070306 (2009).
    [Crossref]
  15. X. Q. Tan, X. Q. Zhang, and J. B. Fang, “Perfect quantum teleportation by four-particle cluster state,” Info Proc. Lett. 116, 347–350 (2016).
    [Crossref]
  16. M. H. Sang, “Bidirectional quantum teleportation by using five-qubit cluster state,” Int. J. Theor. Phys. 55, 1333–1335 (2016).
    [Crossref]
  17. N. Zhao, M. Li, N. Chen, and C. H. Zhu, “Quantum teleportation of eight-qubit state via six-qubit cluster state,” Int. J. Theor. Phys. 57, 516–522 (2018).
    [Crossref]
  18. Q. C. Wu, J. J. Wen, X. Ji, and K. H. Yeon, “Teleportation of three-dimensional single particle state in noninertial frames,” Chin. Phys. B 23, 020303 (2014).
    [Crossref]
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    [Crossref]
  20. B. Artur, I. I. Arkhipov, and S. Jiří, “Localizable entanglement as a necessary resource of controlled quantum teleportation,” Sci. Rep. 8, 15209 (2018).
    [Crossref]
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    [Crossref]
  22. V. Lev, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
    [Crossref]
  23. L. Riccardo, L. S. Braunstein, and P. Stefano, “Finite-resource teleportation stretching for continuous-variable systems,” Sci. Rep. 8, 15267 (2018).
    [Crossref]
  24. J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
    [Crossref]
  25. A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
    [Crossref]
  26. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
    [Crossref]
  27. C. H. Bennett, “Communication via one- and two-particle operators on EPR states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
    [Crossref]
  28. H. V. Nguyen, Z. Babar, D. Alanis, P. Botsinis, D. Chandra, M. A. M. Izhar, S. X. Ng, and L. H. Hanzo, “Towards the quantum internet: generalized quantum network coding for large-scale quantum communication networks,” IEEE Access 5, 17288–17308 (2017).
    [Crossref]
  29. T. Shang, X. J. Zhao, and J. W. Liu, “Quantum network coding based on controlled teleportation,” IEEE Commun. Lett. 18, 865–868 (2014).
    [Crossref]
  30. T. Shang, Z. Pei, X. J. Zhao, and J. W. Liu, “Quantum network coding against pollution attacks,” IEEE Commun. Lett. 20, 1369–1372 (2016).
    [Crossref]
  31. M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “‘Event-ready-detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
    [Crossref]
  32. J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
    [Crossref]
  33. T. Yoshiaki, M. Tanaka, N. Iwasaki, R. Ikuta, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “High-fidelity entanglement swapping and generation of three-qubit GHZ state using asynchronous telecom photon pair sources,” Sci. Rep. 8, 1446 (2018).
    [Crossref]
  34. X. T. Yu, J. Xu, and Z. C. Zhang, “Distributed wireless quantum communication networks,” Chin. Phys. B 22, 090311 (2013).
    [Crossref]
  35. K. Wang, X. T. Yu, S. L. Lu, and Y. X. Gong, “Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation,” Phys. Rev. A 89, 022329 (2014).
    [Crossref]
  36. K. Wang, Y. X. Gong, X. T. Yu, and S. L. Lu, “Addendum to “Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation,” Phys. Rev. A 90, 044302 (2014).
    [Crossref]
  37. Z. Z. Li, G. Xu, X.-B. Chen, X. Sun, and Y.-X. Yang, “Multi-user quantum wireless network communication based on multi-qubit GHZ states,” IEEE Commun. Lett. 20, 2470–2473 (2016).
    [Crossref]
  38. B. S. Shi, G. C. Guo, and Y. K. Jiang, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (2000).
    [Crossref]
  39. M. Y. Wang and F. L. Yan, “Probabilistic chain teleportation of a qutrit-state,” Commun. Theor. Phys. 54, 263–268 (2010).
    [Crossref]
  40. X. Q. Gao, Z. C. Zhang, Y. X. Gong, B. Sheng, and X. T. Yu, “Teleportation of entanglement using a three-particle entangled W state,” J. Opt. Soc. Am. B 34, 142–147 (2017).
    [Crossref]
  41. J. H. Wei, H. Y. Dai, L. Shi, S. H. Zhao, and M. Zhang, “Deterministic quantum controlled teleportation of arbitrary multi-qubit states via partially entangled states,” Int. J. Theor. Phys. 57, 3104–3111 (2018).
    [Crossref]
  42. L. Roa and C. Groiseau, “Probabilistic teleportation without loss of information,” Phys. Rev. A 91, 012344 (2015).
    [Crossref]
  43. M. Jiang, H. Li, Z. K. Zhang, and J. Zeng, “Faithful teleportation via multi-particle quantum states in a network with many agents,” Quantum Inf. Process. 11, 23–40 (2012).
    [Crossref]
  44. X. Q. Tan, X. Q. Zhang, and T. T. Song, “Deterministic quantum teleportation of a particular six-qubit state using six-qubit cluster state,” Int. J. Theor. Phys. 55, 155–160 (2016).
    [Crossref]
  45. J. Heo, C. H. Hong, M. S. Kang, H. J. Yang, J. P. Hong, and S. G. Choi, “Implementation of controlled quantum teleportation with an arbitrator for secure quantum channels via quantum dots inside optical cavities,” Sci. Rep. 7, 14905 (2017).
    [Crossref]
  46. L. H. Shi, X. T. Yu, X. F. Cai, Y. X. Gong, and Z. C. Zhang, “Quantum information transmission in the quantum wireless multihop network based on Werner state,” Chin. Phys. B 24, 247–251 (2015).
    [Crossref]
  47. A. K. Pati and P. Agrawal, “Probabilistic teleportation of a qudit,” Phys. Lett. A 371, 185–189 (2007).
    [Crossref]

2018 (5)

N. Zhao, M. Li, N. Chen, and C. H. Zhu, “Quantum teleportation of eight-qubit state via six-qubit cluster state,” Int. J. Theor. Phys. 57, 516–522 (2018).
[Crossref]

L. Riccardo, L. S. Braunstein, and P. Stefano, “Finite-resource teleportation stretching for continuous-variable systems,” Sci. Rep. 8, 15267 (2018).
[Crossref]

B. Artur, I. I. Arkhipov, and S. Jiří, “Localizable entanglement as a necessary resource of controlled quantum teleportation,” Sci. Rep. 8, 15209 (2018).
[Crossref]

T. Yoshiaki, M. Tanaka, N. Iwasaki, R. Ikuta, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “High-fidelity entanglement swapping and generation of three-qubit GHZ state using asynchronous telecom photon pair sources,” Sci. Rep. 8, 1446 (2018).
[Crossref]

J. H. Wei, H. Y. Dai, L. Shi, S. H. Zhao, and M. Zhang, “Deterministic quantum controlled teleportation of arbitrary multi-qubit states via partially entangled states,” Int. J. Theor. Phys. 57, 3104–3111 (2018).
[Crossref]

2017 (3)

X. Q. Gao, Z. C. Zhang, Y. X. Gong, B. Sheng, and X. T. Yu, “Teleportation of entanglement using a three-particle entangled W state,” J. Opt. Soc. Am. B 34, 142–147 (2017).
[Crossref]

J. Heo, C. H. Hong, M. S. Kang, H. J. Yang, J. P. Hong, and S. G. Choi, “Implementation of controlled quantum teleportation with an arbitrator for secure quantum channels via quantum dots inside optical cavities,” Sci. Rep. 7, 14905 (2017).
[Crossref]

H. V. Nguyen, Z. Babar, D. Alanis, P. Botsinis, D. Chandra, M. A. M. Izhar, S. X. Ng, and L. H. Hanzo, “Towards the quantum internet: generalized quantum network coding for large-scale quantum communication networks,” IEEE Access 5, 17288–17308 (2017).
[Crossref]

2016 (7)

T. Shang, Z. Pei, X. J. Zhao, and J. W. Liu, “Quantum network coding against pollution attacks,” IEEE Commun. Lett. 20, 1369–1372 (2016).
[Crossref]

X. Q. Tan, X. Q. Zhang, and J. B. Fang, “Perfect quantum teleportation by four-particle cluster state,” Info Proc. Lett. 116, 347–350 (2016).
[Crossref]

M. H. Sang, “Bidirectional quantum teleportation by using five-qubit cluster state,” Int. J. Theor. Phys. 55, 1333–1335 (2016).
[Crossref]

L. Zhou and Y. B. Sheng, “Feasible logic Bell-state analysis with linear optics,” Sci. Rep. 6, 20901 (2016).
[Crossref]

E. O. Kiktenko, A. A. Popov, and A. K. Fedorov, “Bidirectional imperfect quantum teleportation with a single Bell state,” Phys. Rev. A 93, 062305 (2016).
[Crossref]

X. Q. Tan, X. Q. Zhang, and T. T. Song, “Deterministic quantum teleportation of a particular six-qubit state using six-qubit cluster state,” Int. J. Theor. Phys. 55, 155–160 (2016).
[Crossref]

Z. Z. Li, G. Xu, X.-B. Chen, X. Sun, and Y.-X. Yang, “Multi-user quantum wireless network communication based on multi-qubit GHZ states,” IEEE Commun. Lett. 20, 2470–2473 (2016).
[Crossref]

2015 (4)

L. Roa and C. Groiseau, “Probabilistic teleportation without loss of information,” Phys. Rev. A 91, 012344 (2015).
[Crossref]

L. H. Shi, X. T. Yu, X. F. Cai, Y. X. Gong, and Z. C. Zhang, “Quantum information transmission in the quantum wireless multihop network based on Werner state,” Chin. Phys. B 24, 247–251 (2015).
[Crossref]

Y. B. Sheng and L. Zhou, “Entanglement analysis for macroscopic Schrödinger’s Cat state,” Europhys. Lett. 109, 40009 (2015).
[Crossref]

S. Hu, W.-X. Cui, D.-Y. Wang, C.-H. Bai, Q. Guo, H.-F. Wang, A.-D. Zhu, and S. Zhang, “Teleportation of a Toffoli gate among distant solid-state qubits with quantum dots embedded in optical microcavities,” Sci. Rep. 5, 11321 (2015).
[Crossref]

2014 (4)

T. Shang, X. J. Zhao, and J. W. Liu, “Quantum network coding based on controlled teleportation,” IEEE Commun. Lett. 18, 865–868 (2014).
[Crossref]

K. Wang, X. T. Yu, S. L. Lu, and Y. X. Gong, “Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation,” Phys. Rev. A 89, 022329 (2014).
[Crossref]

K. Wang, Y. X. Gong, X. T. Yu, and S. L. Lu, “Addendum to “Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation,” Phys. Rev. A 90, 044302 (2014).
[Crossref]

Q. C. Wu, J. J. Wen, X. Ji, and K. H. Yeon, “Teleportation of three-dimensional single particle state in noninertial frames,” Chin. Phys. B 23, 020303 (2014).
[Crossref]

2013 (1)

X. T. Yu, J. Xu, and Z. C. Zhang, “Distributed wireless quantum communication networks,” Chin. Phys. B 22, 090311 (2013).
[Crossref]

2012 (1)

M. Jiang, H. Li, Z. K. Zhang, and J. Zeng, “Faithful teleportation via multi-particle quantum states in a network with many agents,” Quantum Inf. Process. 11, 23–40 (2012).
[Crossref]

2010 (3)

M. Y. Wang and F. L. Yan, “Probabilistic chain teleportation of a qutrit-state,” Commun. Theor. Phys. 54, 263–268 (2010).
[Crossref]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyper-entangled Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

D. Boschi, S. Branca, F. D. Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (2010).
[Crossref]

2009 (2)

J. Dong and J. F. Teng, “Probabilistic controlled teleportation of a triplet W state with combined channel of non-maximally entangled Einstein–Podolsky–Rosen and Greenberger–Horne–Zeilinger states,” Chin. Phys. Lett. 26, 070306 (2009).
[Crossref]

F. L. Yan and T. Yan, “Probabilistic teleportation via a non-maximally entangled GHZ state,” Chin. Sci. Bull. 55, 902–906 (2009).
[Crossref]

2008 (1)

T. J. Wang, H. Y. Zhou, and F. G. Deng, “Quantum state sharing of an arbitrary m-qudit state with two-qudit entanglements and generalized Bell-state measurements,” Phys. A 387, 4716–4722 (2008).
[Crossref]

2007 (1)

A. K. Pati and P. Agrawal, “Probabilistic teleportation of a qudit,” Phys. Lett. A 371, 185–189 (2007).
[Crossref]

2006 (1)

Z. J. Zhang, “Controlled teleportation of an arbitrary n-qubit quantum information using quantum secret sharing of classical message,” Phys. Lett. A 352, 55–58 (2006).
[Crossref]

2005 (1)

K. G. Qi and H. C. Yuan, “Quantum logic networks for controlled teleportation of a single particle via W state,” Chin. Phys. 14, 898–901 (2005).
[Crossref]

2003 (1)

F. L. Yan and D. Wang, “Probabilistic and controlled teleportation of unknown quantum states,” Phys. Lett. A 316, 297–303 (2003).
[Crossref]

2000 (1)

B. S. Shi, G. C. Guo, and Y. K. Jiang, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (2000).
[Crossref]

1998 (1)

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

1997 (1)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eib, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

1996 (1)

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[Crossref]

1995 (2)

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[Crossref]

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[Crossref]

1994 (1)

V. Lev, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[Crossref]

1993 (2)

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “‘Event-ready-detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[Crossref]

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wooters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref]

1992 (1)

C. H. Bennett, “Communication via one- and two-particle operators on EPR states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum mechanical description of physical reality be considered complete,” Phys. Rev. 48, 777–780 (1935).
[Crossref]

Agrawal, P.

A. K. Pati and P. Agrawal, “Probabilistic teleportation of a qudit,” Phys. Lett. A 371, 185–189 (2007).
[Crossref]

Alanis, D.

H. V. Nguyen, Z. Babar, D. Alanis, P. Botsinis, D. Chandra, M. A. M. Izhar, S. X. Ng, and L. H. Hanzo, “Towards the quantum internet: generalized quantum network coding for large-scale quantum communication networks,” IEEE Access 5, 17288–17308 (2017).
[Crossref]

Arkhipov, I. I.

B. Artur, I. I. Arkhipov, and S. Jiří, “Localizable entanglement as a necessary resource of controlled quantum teleportation,” Sci. Rep. 8, 15209 (2018).
[Crossref]

Artur, B.

B. Artur, I. I. Arkhipov, and S. Jiří, “Localizable entanglement as a necessary resource of controlled quantum teleportation,” Sci. Rep. 8, 15209 (2018).
[Crossref]

Babar, Z.

H. V. Nguyen, Z. Babar, D. Alanis, P. Botsinis, D. Chandra, M. A. M. Izhar, S. X. Ng, and L. H. Hanzo, “Towards the quantum internet: generalized quantum network coding for large-scale quantum communication networks,” IEEE Access 5, 17288–17308 (2017).
[Crossref]

Bai, C.-H.

S. Hu, W.-X. Cui, D.-Y. Wang, C.-H. Bai, Q. Guo, H.-F. Wang, A.-D. Zhu, and S. Zhang, “Teleportation of a Toffoli gate among distant solid-state qubits with quantum dots embedded in optical microcavities,” Sci. Rep. 5, 11321 (2015).
[Crossref]

Barenco, A.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[Crossref]

Bennett, C. H.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[Crossref]

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wooters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref]

C. H. Bennett, “Communication via one- and two-particle operators on EPR states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref]

Bernstein, H. J.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[Crossref]

Boschi, D.

D. Boschi, S. Branca, F. D. Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (2010).
[Crossref]

Botsinis, P.

H. V. Nguyen, Z. Babar, D. Alanis, P. Botsinis, D. Chandra, M. A. M. Izhar, S. X. Ng, and L. H. Hanzo, “Towards the quantum internet: generalized quantum network coding for large-scale quantum communication networks,” IEEE Access 5, 17288–17308 (2017).
[Crossref]

Bouwmeester, D.

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eib, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Branca, S.

D. Boschi, S. Branca, F. D. Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (2010).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wooters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref]

Braunstein, L. S.

L. Riccardo, L. S. Braunstein, and P. Stefano, “Finite-resource teleportation stretching for continuous-variable systems,” Sci. Rep. 8, 15267 (2018).
[Crossref]

Cai, X. F.

L. H. Shi, X. T. Yu, X. F. Cai, Y. X. Gong, and Z. C. Zhang, “Quantum information transmission in the quantum wireless multihop network based on Werner state,” Chin. Phys. B 24, 247–251 (2015).
[Crossref]

Chandra, D.

H. V. Nguyen, Z. Babar, D. Alanis, P. Botsinis, D. Chandra, M. A. M. Izhar, S. X. Ng, and L. H. Hanzo, “Towards the quantum internet: generalized quantum network coding for large-scale quantum communication networks,” IEEE Access 5, 17288–17308 (2017).
[Crossref]

Chen, N.

N. Zhao, M. Li, N. Chen, and C. H. Zhu, “Quantum teleportation of eight-qubit state via six-qubit cluster state,” Int. J. Theor. Phys. 57, 516–522 (2018).
[Crossref]

Chen, X.-B.

Z. Z. Li, G. Xu, X.-B. Chen, X. Sun, and Y.-X. Yang, “Multi-user quantum wireless network communication based on multi-qubit GHZ states,” IEEE Commun. Lett. 20, 2470–2473 (2016).
[Crossref]

Choi, S. G.

J. Heo, C. H. Hong, M. S. Kang, H. J. Yang, J. P. Hong, and S. G. Choi, “Implementation of controlled quantum teleportation with an arbitrator for secure quantum channels via quantum dots inside optical cavities,” Sci. Rep. 7, 14905 (2017).
[Crossref]

Cirac, J. I.

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[Crossref]

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wooters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref]

Cui, W.-X.

S. Hu, W.-X. Cui, D.-Y. Wang, C.-H. Bai, Q. Guo, H.-F. Wang, A.-D. Zhu, and S. Zhang, “Teleportation of a Toffoli gate among distant solid-state qubits with quantum dots embedded in optical microcavities,” Sci. Rep. 5, 11321 (2015).
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B. S. Shi, G. C. Guo, and Y. K. Jiang, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (2000).
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J. Heo, C. H. Hong, M. S. Kang, H. J. Yang, J. P. Hong, and S. G. Choi, “Implementation of controlled quantum teleportation with an arbitrator for secure quantum channels via quantum dots inside optical cavities,” Sci. Rep. 7, 14905 (2017).
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[Crossref]

K. Wang, Y. X. Gong, X. T. Yu, and S. L. Lu, “Addendum to “Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation,” Phys. Rev. A 90, 044302 (2014).
[Crossref]

X. T. Yu, J. Xu, and Z. C. Zhang, “Distributed wireless quantum communication networks,” Chin. Phys. B 22, 090311 (2013).
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Figures (5)

Fig. 1.
Fig. 1. Quantum circuit diagram for one-to-one nondestructive qudit teleportation.
Fig. 2.
Fig. 2. Quantum circuit diagram for the $ \textit{CNOT} $ operation.
Fig. 3.
Fig. 3. Teleportation via $ P $ intermediate nodes who share different Bell states with its neighboring nodes.
Fig. 4.
Fig. 4. Quantum circuit diagram for our multihop nondestructive teleportation scheme.
Fig. 5.
Fig. 5. Nondestructive teleportation with the help of three intermediate nodes.

Tables (1)

Tables Icon

Table 1. Comparison between Previous Teleportation Schemes and Ours

Equations (47)

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| χ t = j = 0 d 1 c j | j t ,
| φ A 1 B 1 = k = 0 d 1 a k | k k A 1 B 1 ,
| φ t A 1 B 1 e = | χ t | φ A 1 B 1 | 0 e = ( j = 0 d 1 c j | j t ) ( k = 0 d 1 a k | k k A 1 B 1 ) | 0 e = k = 0 d 1 ( ( j = 0 d 1 c j | j k t A 1 ) a k | k 0 B 1 e ) .
GCNOT | m n = | m | ( m + n ) mod d .
G H = 1 d k , k = 0 d 1 e 2 π i k k / d | k k | .
| φ t A 1 B 1 e = ( G H ) t ( GCNOT ) t A 1 | φ t A 1 B 1 e = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) a s | s B 1 ) | 0 e .
C B 1 e U B 1 = k = 0 d 1 ( ( a min a k | k 0 B 1 e k 0 | + 1 ( a min a k ) 2 | k 0 B 1 e k 1 | ) + ( 1 ( a min a k ) 2 | k 1 B 1 e k 0 | a min a k | k 1 B 1 e k 1 | ) ) .
| φ t A 1 B 1 e = C B 1 e U B 1 | φ t A 1 B 1 e = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ( a min | s 0 B 1 e + a s 2 a min 2 | s 1 B 1 e ) = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ) .
| φ t A 1 B 1 = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) | s B 1 ) = 1 d r , s = 0 d 1 ( | r s t A 1 ( j = 0 d 1 e 2 π i d j r c j | ( s j ) mod d B 1 ) ) .
| φ B 1 = r , s = 0 d 1 ( j = 0 d 1 e 2 π i d j r c j | ( s j ) mod d B 1 ) .
U B 1 rs = j = 0 d 1 e 2 π i d j r | j ( s j ) mod d | × ( r , s = 0 , 1 , , d 1 ) .
| φ B 1 = U B 1 rs | φ B 1 = j = 0 d 1 c j | j B 1 .
| φ t A 1 B 1 = 1 d s = 0 d 1 ( r = 0 d 1 ( c r j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ( a s 2 a min 2 | s B 1 ) = 1 d s = 0 d 1 ( r = 0 d 1 ( c r j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ) .
( G H ) 1 = 1 d k , k = 0 d 1 e 2 π i k k / d | k k | .
( G C N ) 1 | m n = | m | ( n m ) mod d .
| φ t A 1 B 1 = ( G C N ) t A 1 1 ( G H ) t 1 | φ t A 1 B 1 = r = 0 d 1 ( c r | r t ) ( s = 0 d 1 a s 2 a min 2 | s s A 1 B 1 ) .
| φ A q B q = j = 0 d 1 a qj | j j A q B q ( q = 1 , 2 , , P + 1 ) ,
| φ A 1 B 1 A P + 1 B P + 1 = q = 1 P + 1 ( j = 0 d 1 a qj | j j A q B q ) = ( 1 d ) P m 1 , n 1 = 0 d 1 m 2 , n 2 = 0 d 1 × m P , n P = 0 d 1 | ϕ m 1 n 1 B 1 A 2 | ϕ m 2 n 2 B 2 A 3 | ϕ m P n P B P A P + 1 × ( U m 1 n 1 1 ) B p + 1 ( U m 2 n 2 1 ) B p + 1 ( U m P n P 1 ) B p + 1 | φ A 1 B P + 1 ,
| φ A 1 B P + 1 = j = 0 d 1 ( ( q = P + 1 1 a q , ( k q + j ) mod d ) | j j A 1 B P + 1 ) ,
b j = q = P + 1 1 a q , ( k q + j ) mod d ( j = 0 , 1 , , d 1 ) .
| φ A 1 B P + 1 = j = 0 d 1 ( ( q = P + 1 1 a q , ( k q + j ) mod d ) | j j A 1 B P + 1 ) = j = 0 d 1 ( b j | j j A 1 B P + 1 ) ,
| φ t A 1 B P + 1 e = ( G H ) t ( GCNOT ) t A 1 | φ t A 1 B P + 1 e = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ( b s | s B P + 1 ) = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ) | 0 e .
C B P + 1 e U B P + 1 = k = 0 d 1 ( ( b m i n b k | k 0 B P + 1 e k 0 | + 1 ( b m i n b k ) 2 | k 0 B P + 1 e k 1 | ) + ( 1 ( b m i n b k ) 2 | k 1 B P + 1 e k 0 | b m i n b k | k 1 B P + 1 e k 1 | ) ) .
| φ t A 1 B P + 1 e = C B P + 1 , e U B P + 1 | φ t A 1 B P + 1 e = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ( b min | s 0 B P + 1 e + ( b s ) 2 ( b min ) 2 | s 1 B P + 1 e ) = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ) .
| φ 0 t A 1 B P + 1 = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) | s B P + 1 ) = 1 d r , s = 0 d 1 ( | r s t A 1 ( j = 0 d 1 e 2 π i d j r c j | ( s j ) mod d B P + 1 ) ) .
| φ B P + 1 = r , s = 0 d 1 ( j = 0 d 1 e 2 π i d j r c j | ( s j ) mod d B P + 1 ) .
U B P + 1 rs = j = 0 d 1 e 2 π i d j r | j ( s j ) mod d | × ( r , s = 0 , 1 , , d 1 ) .
| φ B P + 1 = U B P + 1 rs | φ B P + 1 = j = 0 d 1 c j | j B P + 1 .
| φ t A 1 B P + 1 = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ( ( b s ) 2 ( b min ) 2 | s B P + 1 ) = 1 d s = 0 d 1 ( r = 0 d 1 c r ( j = 0 d 1 e 2 π i d j r | j , ( r + s ) mod d t A 1 ) ) .
| φ t A 1 B P + 1 = ( G C N ) 1 t A 1 ( G H ) t 1 | φ t A 1 B P + 1 = 1 d r = 0 d 1 ( c r | r t ) s = 0 d 1 ( ( ( b s ) 2 ( b min ) 2 | s s A 1 B P + 1 ) ) .
| χ t = c 0 | 0 + c 1 | 1 + c 2 | 2 .
| φ 1 A 1 B 1 = a 10 | 00 + a 11 | 11 + a 12 | 22 , | φ 2 A 2 B 2 = a 20 | 00 + a 21 | 11 + a 22 | 22 , | φ 3 A 3 B 3 = a 30 | 00 + a 31 | 11 + a 32 | 22 , | φ 4 A 4 B 4 = a 40 | 00 + a 41 | 11 + a 42 | 22 .
| φ A 1 B 1 A 2 B 2 A 3 B 3 A 4 B 4 = q = 1 4 | φ q A q B q = k 4 = 0 2 k 3 = 0 2 k 2 = 0 2 k 1 = 0 2 a 4 , k 4 a 3 , k 3 a 2 , k 2 a 1 , k 1 × | k 1 , k 1 , k 2 , k 2 , k 3 , k 3 , k 4 , k 4 A 1 B 1 A 2 B 2 A 3 B 3 A 4 B 4 = ( 1 3 ) 3 m 1 , n 1 = 0 2 m 2 , n 2 = 0 2 m 3 , n 3 = 0 2 × | ϕ m 1 n 1 B 1 A 2 | ϕ m 2 n 2 B 2 A 3 | ϕ m 3 n 3 B 3 A 4 × ( U m 1 n 1 1 U m 2 n 2 1 U m 3 n 3 1 ) B 4 | φ A 1 B 4 .
U B 4 o p e r = q = 1 3 ( U m q n q ) B 4 = ( U 10 U 12 U 21 ) B 4 = ( j = 0 2 | ( j + 1 ) mod 3 B 4 j | ) × ( j = 0 2 e 2 π i 3 2 j | ( j + 1 ) mod 3 B 4 j | ) × ( j = 0 2 e 2 π i 3 j | ( j + 2 ) mod 3 B 4 j | ) = e 8 π i 3 | 1 B 4 0 | + e 2 π i 3 | 2 B 4 1 | + e 8 π i 3 | 0 B 4 2 | .
| φ A 1 B 4 = j = 0 2 ( ( q = 4 1 a q , ( k q + j ) mod 3 ) | j j A 1 B 4 ) = a 40 a 3 , ( k 3 ) a 2 , ( k 2 ) a 1 , ( k 1 ) | 00 A 1 B 4 + a 41 a 3 , ( k 3 + 1 ) mod 3 a 2 , ( k 2 + 1 ) mod 3 a 1 , ( k 1 + 1 ) mod 3 | 11 A 1 B 4 + a 42 a 3 , ( k 3 + 2 ) mod 3 a 2 , ( k 2 + 2 ) mod 3 a 1 , ( k 1 + 2 ) mod 3 | 22 A 1 B 4 ,
| φ A 1 B 4 = a 40 a 3 , ( 0 m 3 ) mod 3 a 2 , ( ( 0 m 3 ) mod 3 m 2 ) mod 3 × a 1 , ( ( ( 0 m 3 ) mod 3 m 2 ) mod 3 m 1 ) mod 3 | 00 + a 41 a 3 , ( 1 m 3 ) mod 3 a 2 , ( ( 1 m 3 ) mod 3 m 2 ) mod 3 × a 1 , ( ( ( 1 m 3 mod 3 ) m 2 mod 3 ) m 1 mod 3 ) | 11 + a 42 a 3 , ( 2 m 3 ) mod 3 a 2 , ( ( 2 m 3 ) mod 3 m 2 ) mod 3 × a 1 , ( ( ( 2 m 3 mod 3 ) m 2 mod 3 ) m 1 mod 3 ) | 22 = a 40 a 31 a 20 a 12 | 00 + a 41 a 32 a 21 a 10 | 11 + a 42 a 30 a 22 a 11 | 22 .
| φ A 1 B 4 = a 40 a 31 a 20 a 12 | 00 + a 41 a 32 a 21 a 10 | 11 + a 42 a 30 a 22 a 11 | 22 = b 0 | 00 + b 1 | 11 + b 2 | 22 .
| φ t A 1 B e = ( ( c 0 | 0 + c 1 | 1 + c 2 | 2 ) t ( b 0 | 00 + b 1 | 11 + b 2 | 22 ) A 1 B 4 ) | 0 e .
| φ t A 1 B 4 e = C B 4 e U B 4 ( G H ) t ( GCNOT ) t A 1 | φ t A 1 B 4 e = 1 3 s = 0 2 ( r = 0 2 c r ( j = 0 2 e 2 π i j r | j , ( r + s ) mod 3 t A 1 ) ( b min | s 0 B 4 e + b s 2 b min 2 | s 1 B 4 e ) = 1 3 s = 0 2 ( r = 0 2 c r ( j = 0 2 e 2 π i j r | j , ( r + s ) mod 3 t A 1 ) ) .
| φ 0 t A 1 B 4 e = 1 3 s = 0 2 ( r = 0 2 c r ( j = 0 2 e 2 π i 3 j r | j , ( r + s ) mod 3 t , A 1 ) | s B 4 ) = 1 3 r , s = 0 2 ( | r s t A 1 ( j = 0 2 e 2 π i 3 j r c j | ( s j ) mod 3 B 4 ) ) .
| φ B 4 = j = 0 2 e 2 π i 3 j r c j | ( s j ) mod 3 B 4 = j = 0 2 e 4 π i 3 j c j | ( 2 j ) mod 3 B 4 .
| φ 1 t A 1 B 2 = 1 3 s = 0 2 ( r = 0 2 c r ( j = 0 2 e 2 π i 3 j r | j , ( r + s ) mod 3 t A 1 ) ( b s 2 b min 2 | s B 4 ) = 1 3 s = 0 2 ( r = 0 2 c r ( j = 0 2 e 2 π i 3 j r | j , ( r + s ) mod 3 t A 1 ) ) .
| φ 1 t A 1 B 4 = ( c 0 | 0 + c 1 | 1 + c 2 | 2 ) t ( b 0 2 b min 2 | 00 A 1 B 4 + b 1 2 b min 2 | 11 A 1 B 4 + b 2 2 b min 2 | 22 A 1 B 4 ) .
C t o t a l q u d i t = 2 P + 2 ( q u d i t s ) .
C t o t a l c b i t = 2 log 2 d ( P + 1 ) ( b i t s ) .
D t o t a l = D 1 + D 3 + max ( D 4 , D 4 ) = ( D GBM + D t r a n s ( 1 ) + D u o p e r ) + ( D C + D e m e a s + D t r a n s ( 2 ) ) + max ( D t A 1 m e a s + D U B P + 1 rs , D G H 1 + D G C N 1 ) .
D h o p b y h o p = P ( D GBM + D t r a n s ( 1 ) + D u o p e r ) + ( D C + D e m e a s + D t r a n s ( 2 ) ) + max ( D t A 1 m e a s + D U B P + 1 rs , D G H 1 + D G C N 1 ) .

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