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Deterministic joint remote preparation of an equatorial hybrid state via high-dimensional Einstein–Podolsky–Rosen pairs: active versus passive receiver

  • Cao Thi Bich
  • Le Thanh Dat
  • Nguyen Van Hop
  • Nguyen Ba An
Article
  • 75 Downloads

Abstract

Entanglement plays a vital and in many cases non-replaceable role in the quantum network communication. Here, we propose two new protocols to jointly and remotely prepare a special so-called bipartite equatorial state which is hybrid in the sense that it entangles two Hilbert spaces with arbitrary different dimensions D and N (i.e., a type of entanglement between a quDit and a quNit). The quantum channels required to do that are however not necessarily hybrid. In fact, we utilize four high-dimensional Einstein–Podolsky–Rosen pairs, two of which are quDit–quDit entanglements, while the other two are quNit–quNit ones. In the first protocol the receiver has to be involved actively in the process of remote state preparation, while in the second protocol the receiver is passive as he/she needs to participate only in the final step for reconstructing the target hybrid state. Each protocol meets a specific circumstance that may be encountered in practice and both can be performed with unit success probability. Moreover, the concerned equatorial hybrid entangled state can also be jointly prepared for two receivers at two separated locations by slightly modifying the initial particles’ distribution, thereby establishing between them an entangled channel ready for a later use.

Keywords

Deterministic joint remote state preparation Equatorial state Hybrid dimension High-dimensional EPR pair Active receiver Passive receiver 

Notes

Acknowledgements

This work is supported by the Vietnam Foundation for Science and Technology Development (NAFOSTED) under a Project No. 103.01-2017.08.

References

  1. 1.
    Born, M.: Letter from Albert Einstein to Max Born Physik im Wandel Meiner Zeit, p. 228. Springer, Berlin (1983)CrossRefGoogle Scholar
  2. 2.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  3. 3.
    Bennett, B.H, Brassard, G.: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, p. 175. IEEE, New York (1984)Google Scholar
  4. 4.
    Bennett, C.H., Wiesner, S.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bennett, B.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science. IEEE Press, Los Alamitos (1994)Google Scholar
  7. 7.
    Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)ADSCrossRefGoogle Scholar
  9. 9.
    Devetak, I., Berger, T.: Low-entanglement remote state preparation. Phys. Rev. Lett. 87, 197901 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    Zeng, B., Zhang, P.: Remote-state preparation in higher dimension and the parallelizable manifold \(S^{n-1}\). Phys. Rev. A 65, 022316 (2002)ADSCrossRefGoogle Scholar
  11. 11.
    Audenaert, K., Plenio, M.B., Eisert, J.: Entanglement cost under positive-partial-transpose-preserving operations. Phys. Rev. Lett. 90, 027901 (2003)ADSCrossRefGoogle Scholar
  12. 12.
    Peng, X.H., Zhu, X.W., Fang, X., Feng, M., Liu, M.L., Gao, K.: Experimental implementation of remote state preparation by nuclear magnetic resonance. Phys. Lett. A 306, 271 (2003)ADSCrossRefGoogle Scholar
  13. 13.
    Xiang, G.Y., Li, J., Yu, B., Guo, G.C.: Remote preparation of mixed states via noisy entanglement. Phys. Rev. A 72, 012315 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    Xia, Y., Song, J., Song, S.H.: Multiparty remote state preparation. J. Phys. B At. Mol. Opt. Phys. 40, 3719 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    An, N.B., Kim, J.: Joint remote state preparation. J. Phys. B At. Mol. Opt. Phys. 41, 095501 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    An, N.B., Kim, J.: Collective remote state preparation. Int. J. Quantum Inf. 6, 1051 (2008)CrossRefzbMATHGoogle Scholar
  17. 17.
    An, N.B.: Joint remote preparation of a general two-qubit state. J. Phys. B At. Mol. Opt. Phys. 42, 125501 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    An, N.B.: Joint remote state preparation via W and W-type states. Opt. Commun. 283, 4113 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    Chen, Q.Q., Xia, Y., Song, J., An, N.B.: Joint remote state preparation of a W-type state via W-type states. Phys. Lett. A 374, 4483 (2010)ADSCrossRefzbMATHGoogle Scholar
  20. 20.
    An, N.B., Bich, C.T., Don, N.V.: Deterministic joint remote state preparation. Phys. Lett. A 375, 3570 (2011)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Chen, Q.Q., Xia, Y., An, N.B.: Joint remote preparation of an arbitrary three-qubit state via EPR-type pairs. Opt. Commun. 284, 2617 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    Zhan, Y.B., Hu, B.L., Ma, P.C.: Joint remote preparation of four-qubit cluster-type states. J. Phys. B At. Mol. Opt. Phys. 44, 095501 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Wang, Z.Y.: Joint remote preparation of a multi-qubit GHZ-class state via bipartite entanglements. Int. J. Quantum Inf. 9, 809 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Xiao, X.Q., Liu, J.M., Zeng, G.: Joint remote state preparation of arbitrary two- and three-qubit states. J. Phys. B At. Mol. Opt. Phys. 44, 075501 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    Xia, Y., Chen, Q.Q., An, N.B.: Deterministic joint remote preparation of an arbitrary three-qubit state via Einstein–Podolsky–Rosen pairs with a passive receiver. J. Phys. A Math. Theor. 45, 335306 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Luo, M.X., Chen, X.B., Yang, Y.X., Niu, X.X.: Experimental architecture of joint remote state preparation. Quantum Inf. Process. 11, 751 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Jiang, M., Jiang, F.: Deterministic joint remote preparation of arbitrary multi-qudit states. Phys. Lett. A 377, 2524 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Li, H., Ping, Y., Pan, X., Luo, M., Zhang, Z.: Joint remote preparation of an arbitrary three-qubit state with mixed resources. Int. J. Theor. Phys. 52, 4265 (2013)CrossRefzbMATHGoogle Scholar
  29. 29.
    Ai, L.T., Nong, L., Zhou, P.: Efficient joint remote preparation of an arbitrary m-qudit state with partially entangled states. Int. J. Theor. Phys. 53, 159 (2014)CrossRefzbMATHGoogle Scholar
  30. 30.
    Yu, R.F., Lin, Y.J., Zhou, P.: Joint remote preparation of arbitrary two- and three-photon state with linear-optical elements. Quantum Inf. Process. 15, 4785 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Chen, N., Quan, D.X., Zhu, C.H., Liand, J.Z., Pei, C.X.: Deterministic joint remote state preparation via partially entangled quantum channel. Int. J. Quantum Inform. 14, 1650015 (2016)ADSCrossRefzbMATHGoogle Scholar
  32. 32.
    Wang, M.M., Qu, Z.G.: Effect of quantum noise on deterministic joint remote state preparation of a qubit state via a GHZ channel. Quantum Inf. Process. 15, 4805 (2016)ADSCrossRefzbMATHGoogle Scholar
  33. 33.
    Zhao, H.X., Huang, L.: Effects of noise on joint remote state preparation of an arbitrary equatorial two-qubit state. Int. J. Theor. Phys. 56, 720 (2017)CrossRefzbMATHGoogle Scholar
  34. 34.
    Adepoju, A.G., Falaye, B.J., Sun, G.H., Nieto, O.C., Dong, S.H.: Joint remote state preparation of two-qubit equatorial state in quantum noisy channels. Phys. Lett. A 381, 581 (2017)ADSCrossRefGoogle Scholar
  35. 35.
    Wang, X.Y., Mo, Z.W.: Bidirectional controlled joint remote state preparation via a seven-qubit entangled state. Int. J. Theor. Phys. 56, 1052 (2017)CrossRefzbMATHGoogle Scholar
  36. 36.
    Bandyopadhyay, S., Boykin, P.O., Roychowdhury, V., Vatan, F.: A new proof for the existence of mutually unbiased bases. Algorithmica 34, 512 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Durt, T., Englert, B.G., Bengtsson, I., Zyczkowski, K.: On mutually unbiased bases. Int. J. Quantum Inf. 08, 535 (2010)CrossRefzbMATHGoogle Scholar
  38. 38.
    Pasquinucci, H.B., Peres, A.: Quantum cryptography with 3-state systems. Phys. Rev. Lett. 85, 3313 (2000)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Pasquinucci, H.B., Tittel, W.: Quantum cryptography using larger alphabets. Phys. Rev. A 61, 06230 (2000)MathSciNetGoogle Scholar
  40. 40.
    Bourennane, M., Karlsson, A., Björk, G.: Quantum key distribution using multilevel encoding. Phys. Rev. A 64, 012306 (2001)ADSCrossRefGoogle Scholar
  41. 41.
    Bruß, D., Macchiavello, C.: Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88, 127901 (2002)ADSCrossRefGoogle Scholar
  42. 42.
    Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using \(\mathit{d}\) -level systems. Phys. Rev. Lett. 88, 127902 (2002)ADSCrossRefGoogle Scholar
  43. 43.
    Walborn, S.P., Lemelle, D.S., Almeida, M.P., Souto Ribeiro, P.S.: Quantum key distribution with higher-order alphabets using spatially encoded qudits. Phys. Rev. Lett. 96, 090501 (2006)ADSCrossRefGoogle Scholar
  44. 44.
    Kaszlikowski, D., Gnaciński, P., Zukowski, M., Miklaszewski, W., Zeilinger, A.: Violations of local realism by two entangled \(N\)-dimensional systems are stronger than for two qubits. Phys. Rev. Lett. 85, 4418 (2000)ADSCrossRefGoogle Scholar
  45. 45.
    Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Vértesi, T., Pironio, S., Brunner, N.: Closing the detection loophole in Bell experiments using qudits. Phys. Rev. Lett. 104, 060401 (2010)CrossRefGoogle Scholar
  47. 47.
    Lee, N., Benichi, H., Takeno, Y., Takeda, S., Webb, J., Huntington, E., Furusawa, A.: Teleportation of nonclassical wave packets of light. Science 332, 330 (2011)ADSCrossRefGoogle Scholar
  48. 48.
    Lee, S.W., Jeong, H.: Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits. Phys. Rev. A 87, 022326 (2013)ADSCrossRefGoogle Scholar
  49. 49.
    Park, K., Lee, S.W., Jeong, H.: Quantum teleportation between particlelike and fieldlike qubits using hybrid entanglement under decoherence effects. Phys. Rev. A 86, 062301 (2012)ADSCrossRefGoogle Scholar
  50. 50.
    Kwon, H., Jeong, H.: Violation of the Bell–Clauser-Horne-Shimony-Holt inequality using imperfect photodetectors with optical hybrid states. Phys. Rev. A 88, 052127 (2013)ADSCrossRefGoogle Scholar
  51. 51.
    Costanzo, L.S., Zavatta, A., Grandi, S., Bellini, M., Jeong, H., Kang, M., Lee, S.W., Ralph, T.C.: Experimental hybrid entanglement between quantum and classical states of light. Int. J. Quantum Inf. 12, 1560015 (2014)CrossRefGoogle Scholar
  52. 52.
    Kwon, H., Jeong, H.: Generation of hybrid entanglement between a single-photon polarization qubit and a coherent state. Phys. Rev. A 91, 012340 (2015)ADSCrossRefGoogle Scholar
  53. 53.
    Podoshvedov, A.S.: Elementary quantum gates in different bases. Quantum Inf. Process. 15, 3967 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    Tao, Y.H., Nan, H., Zhang, J., Fei, S.M.: Mutually unbiased maximally entangled bases in \(\cal{C}^{d} \otimes \cal{C}^{dk}\). Quantum Inf. Process. 14, 2291 (2015)ADSCrossRefGoogle Scholar
  55. 55.
    Luo, L., Li, X., Tao, Y.: Two types of maximally entangled bases and their mutually unbiased Property in \(\cal{C}^{d} \otimes \cal{C}^{d^{^{\prime }}}\). Int. J. Theor. Phys. 55, 5069 (2016)CrossRefzbMATHGoogle Scholar
  56. 56.
    Cai, T., Jiang, M.: Optimal joint remote state preparation of arbitrary equatorial multi-qudit states. Int. J. Theor. Phys. 56, 781 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  57. 57.
    Greenberger, D.M., Horne, M.A., Zeilinger, A.: Bell’s Theorem Quantum Theory and Conceptions of the Universe. Kluwer, Dordrecht (1989)Google Scholar
  58. 58.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSCrossRefzbMATHGoogle Scholar
  59. 59.
    Zaidi, H.A., van Loock, P.: Beating the one-half limit of ancilla-free linear optics Bell measurements. Phys. Rev. Lett. 110, 260501 (2013)ADSCrossRefGoogle Scholar
  60. 60.
    Ewert, F., van Loock, P.: 3/4-efficient Bell measurement with passive linear optics and unentangled ancillae. Phys. Rev. Lett. 113, 140403 (2014)ADSCrossRefGoogle Scholar
  61. 61.
    Lee, S.W., Park, K., Ralph, T.C., Jeong, H.: Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing. Phys. Rev. Lett. 114, 123603 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Theoretical Physics, Institute of PhysicsVietnam Academy of Science and Technology (VAST)Cau GiayVietnam
  2. 2.Physics DepartmentHanoi National University of EducationCau GiayVietnam
  3. 3.Thang Long Institute of Mathematics and Applied Sciences (TIMAS)Thang Long University (TLU)Hoang Mai DistrictVietnam

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