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Recovering information in probabilistic quantum teleportation

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Abstract

In this paper we redesign the probabilistic teleportation scheme considered in Phys. Rev. A61, 034301 (2000) by Wan-Li Li et al., where the optimal state extraction protocol complements the basic teleportation process with a partially entangled pure state channel, in order to transfer the unknown state with fidelity 1. Unlike that scheme, where the information of the unknown state is lost if the state extraction fails, our proposal teleports exactly and optimally an unknown state, and allows to recover faithfully that state when the process has not succeeded. In order to study the resilience of the scheme, we apply it to the teleportation problem through a quantum channel in a mixed state with pure dephasing. We find that a successful process transfers an unfaithful state, namely, the outcome state acquires the decoherence of the channel, but the unknown state is recovered by the sender with fidelity 1 if the teleportation fails. In addition, in this case, the fidelity of the teleported state has quantum features only if the channel has an amount of entanglement different from zero.

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References

  1. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70(13), 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  2. D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Experimental quantum teleportation, Nature 390(6660), 575 (1997)

    Article  ADS  Google Scholar 

  3. D. Boschi, S. Branca, F. De 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(6), 1121 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  4. X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, Quantum teleportation of multiple degrees of freedom of a single photon, Nature 518(7540), 516 (2015)

    Article  ADS  Google Scholar 

  5. N. Gisin, Quantum-teleportation experiments turn 20, Nature 552(7683), 42 (2017)

    Article  ADS  Google Scholar 

  6. R. Lo Franco and G. Compagno, Indistinguishability of elementary systems as a resource for quantum information processing, Phys. Rev. Lett. 120(24), 240403 (2018)

    Article  ADS  Google Scholar 

  7. J. G. Ren, P. Xu, H. L. Yong, L. Zhang, Sh. K. Liao, et al., Ground-to-satellite quantum teleportation, Nature 549(7670), 70 (2017)

    Article  ADS  Google Scholar 

  8. H. Krauter, D. Salart, C. A. Muschik, J. M. Petersen, H. Shen, T. Fernholz, and E. S. Polzik, Deterministic quantum teleportation between distant atomic objects, Nat. Phys. 9(7), 400 (2013)

    Article  Google Scholar 

  9. Sh. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, Deterministic quantum teleportation of photonic quantum bits by a hybrid technique, Nature 500(7462), 315 (2013)

    Article  ADS  Google Scholar 

  10. K. S. Chou, J. Z. Blumoff, C. S. Wang, P. C. Reinhold, C. J. Axline, Y. Y. Gao, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, Deterministic teleportation of a quantum gate between two logical qubits, Nature 561, 368 (2018)

    Article  ADS  Google Scholar 

  11. K. Wang, X. T. Yu, and Z. C. Zhang, Two-qubit entangled state teleportation via optimal POVM and partially entangled GHZ state, Front. Phys. 13, 130320 (2018)

    Article  Google Scholar 

  12. G. Brassard, S. L. Braunstein, and R. Cleve, Teleportation as a quantum computation, Physica D 120(1–2), 43 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  13. D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402(6760), 390 (1999)

    Article  ADS  Google Scholar 

  14. S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, and S. L. Braunstein, Advances in quantum teleportation, Nat. Photonics 9(10), 641 (2015)

    Article  ADS  Google Scholar 

  15. X. F. Cai, X. T. Yu, L. H. Shi, and Z. C. Zhang, Partially entangled states bridge in quantum teleportation, Front. Phys. 9, 646 (2014)

    Article  Google Scholar 

  16. X. Q. Gao, Z. C. Zhang, and B. Sheng, Multi-hop teleportation in a quantum network based on mesh topology, Front. Phys. 13, 130314 (2018)

    Article  Google Scholar 

  17. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 76(5), 722 (1996)

    Article  ADS  Google Scholar 

  18. M. Horodecki, P. Horodecki, and R. Horodecki, General teleportation channel, singlet fraction, and quasidistillation, Phys. Rev. A 60(3), 1888 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  19. L. Roa, R. Gómez, A. Muñoz, G. Rai, and M. Hecker, Entanglement thresholds for displaying the quantum nature of teleportation, Ann. Phys. 371, 228 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  20. L. Roa, M. L. Ladrón de Guevara, M. Soto-Moscoso, and P. Catalan, The joint measurement entanglement can significantly offset the effect of a noisy channel in teleportation, J. Phys. A: Math. Theor. 51(21), 215301 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  21. T. Mor and P. Horodecki, Teleportation via generalized measurements, and conclusive teleportation, arXiv: quant-ph/9906039 (1999)

  22. S. Bandyopadhyay, Teleportation and secret sharing with pure entangled states, Phys. Rev. A 62(1), 012308 (2000)

    Article  ADS  Google Scholar 

  23. W. L. Li, C. F. Li, and G. C. Guo, Probabilistic teleportation and entanglement matching, Phys. Rev. A 61, 034301 (2000)

    Article  ADS  Google Scholar 

  24. P. Agrawal and A. K. Pati, Probabilistic quantum teleportation, Phys. Lett. A 305(1–2), 12 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  25. L. Roa, A. Delgado, and I. Fuentes-Guridi, Optimal conclusive teleportation of quantum states, Phys. Rev. A 68(2), 022310 (2003)

    Article  ADS  Google Scholar 

  26. L. Roa and C. Groiseau, Probabilistic teleportation without loss of information, Phys. Rev. A 91(1), 012344 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  27. L. Roa, A. Muñoz, A. Hutin, and M. Hecker, Threefold entanglement matching, Quantum Inform. Process. 14(11), 4113 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  28. T. Rashvand, Teleporting an unknown quantum state with unit fidelity and unit probability via a non-maximally entangled channel and an auxiliary system, Quantum Inform. Process. 15(11), 4839 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  29. P. Y. Xiong, X. T. Yu, H. T. Zhan, and Z. C. Zhang, Multiple teleportation via partially entangled GHZ state, Front. Phys. 11, 110303 (2016)

    Article  Google Scholar 

  30. L. Y. Hsu, Optimal information extraction in probabilistic teleportation, Phys. Rev. A 66(1), 012308 (2002)

    Article  ADS  Google Scholar 

  31. M. D. G. Ramírez, B. J. Falaye, G. H. Sun, M. Cruz-Irisson, and S. H. Dong, Quantum teleportation and information splitting via four-qubit cluster state and a Bell state, Front. Phys. 12(5), 120306 (2017)

    Article  Google Scholar 

  32. J. L. Skinner and D. Hsu, Pure dephasing of a two-level system, J. Phys. Chem. 90(21), 4931 (1986)

    Article  Google Scholar 

  33. F. K. Wilhelm, Quantum oscillations in the spin-boson model, reduced visibility from non-Markovian effects and initial entanglement, New J. Phys. 10(11), 115011 (2008)

    Article  ADS  Google Scholar 

  34. B. Bellomo, G. Compagno, A. D’Arrigo, G. Falci, R. Lo Franco, and E. Paladino, Entanglement degradation in the solid state: Interplay of adiabatic and quantum noise, Phys. Rev. A 81(6), 062309 (2010)

    Article  ADS  Google Scholar 

  35. L. Mazzola, B. Bellomo, R. Lo Franco, and G. Compagno, Connection among entanglement, mixedness, and nonlocality in a dynamical context, Phys. Rev. A 81(5), 052116 (2010)

    Article  ADS  Google Scholar 

  36. B. Aaronson, R. Lo Franco, and G. Adesso, Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence, Phys. Rev. A 88(1), 012120 (2013)

    Article  ADS  Google Scholar 

  37. W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80(10), 2245 (1998)

    Article  ADS  Google Scholar 

  38. S. Hill and W. K. Wootters, Entanglement of a pair of quantum bits, Phys. Rev. Lett. 78(26), 5022 (1997)

    Article  ADS  Google Scholar 

  39. A. Uhlmann, The “transition probability” in the state space of a *-algebra, Rep. Math. Phys. 9(2), 273 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  40. R. Jozsa, Fidelity for mixed quantum states, J. Mod. Opt. 41(12), 2315 (1994)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by FONDECyT under grant No. 1161631. A. M. thanks to CONICyT.

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Authors and Affiliations

  1. Departamento de Física, Universidad de Conceptión, Casilla 160-C, Conceptión, Chile

    Luis Roa & Ariana Muñoz

  2. Departamento de Física, Universidad Católica del Norte, Angamos 0610, Antofagasta, Chile

    Andrea Espinoza & María L. Ladrón de Guevara

  3. Facultad de Ingeniería, Universidad Autónoma de Chile, 5 Poniente 1670, Talca, Chile

    Ariana Muñoz

Authors
  1. Luis Roa
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  2. Andrea Espinoza
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  3. Ariana Muñoz
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  4. María L. Ladrón de Guevara
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Correspondence to María L. Ladrón de Guevara.

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Roa, L., Espinoza, A., Muñoz, A. et al. Recovering information in probabilistic quantum teleportation. Front. Phys. 14, 61602 (2019). https://doi.org/10.1007/s11467-019-0939-7

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