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Two-Way Remote Preparations of Inequivalent Quantum States Under a Common Control

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Abstract

In this paper we design a deterministic controllable quantum communication protocol for remotely preparing three-qubit GHZ-type and four-qubit W-type entangled states at two different locations at the same time. Two parties (the preparers) along with a third party (the controller) are connected through a proper multipartite entangled resource. The states to be prepared are not physically available, only the classical information of each state is known by a party who intends to remotely prepare it at the end of the other party under the same control of a third party. Concretely, it is a multi-tasking protocol in which remote preparations of the two inequivalent states are accomplished not only simultaneously but also controllably through execution of a single protocol by utilizing an eleven-qubit entangled state as shared quantum resource. We also propose a generation process of the multipartite quantum resource used.

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References

  1. Bennett, C.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, 1895–1899 (1993)

    ADS  MathSciNet  MATH  Google Scholar 

  2. Lo, H.K.: Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)

    ADS  Google Scholar 

  3. Bennett, C.H., Divincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)

    ADS  Google Scholar 

  4. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2001)

    ADS  Google Scholar 

  5. Hayashi, A., Hashimoto, T., Horibe, M.: Remote state preparation without oblivious conditions. Phys. Rev. A 67, 052302 (2003)

    ADS  Google Scholar 

  6. Berry, D.W., Sanders, B.C.: Optimal remote state preparation. Phys. Rev. Lett. 90, 057901 (2003)

    ADS  Google Scholar 

  7. Ye, M.Y., Zhang, Y.S., Guo, G.C.: Faithful remote state preparation using finite classical bits and a nonmaximally entangled state. Phys. Rev. A 69, 022310 (2004)

    ADS  Google Scholar 

  8. Wang, D., Liu, Y.-M., Zhang, Z.-J.: Remote preparation of a class of three-qubit states. Opt. Commun. 281, 871–875 (2008)

    ADS  Google Scholar 

  9. Panigrahi, P.K., Karumnchi, S., Muralidharan, S.: Minimal Classical communication and measurement complexity for quantum information splitting of a two-qubit state. Pramana J. Phys. 73, 499–504 (2009)

    ADS  Google Scholar 

  10. Wang, D.: Remote preparation of an arbitrary two-particle pure state via non-maximally entangled states and positive operator-valued measurement. Int. J. Quantum Inf. 8, 1265–1275 (2010)

    MATH  Google Scholar 

  11. Nguyen, B.A., Cao, T.B., Nung, V.D., Kim, J.: Remote state preparation with unit success probability. Adv. Nat. Sci.: Nanosci. Nanotechnol 2, 035009 (2011)

    ADS  Google Scholar 

  12. Wang, D., Ye, L.: Optimizing scheme for remote preparation of four-particle cluster-like entangled states. Int. J. Theor. Phys. 50, 2748–2757 (2011)

    MATH  Google Scholar 

  13. Zhan, Y.-B., Fu, H., Li, X.-W., Ma, P.-C.: Deterministic remote preparation of a four-qubit cluster-type entangled state. Int. J. Theor. Phys. 52, 2615–2622 (2013)

    MathSciNet  MATH  Google Scholar 

  14. Zhao, S.-Y., Fu, H., Li, X.-W., Chen, G.-B., Ma, P.-C., Zhan, Y.-B.: Efficient and economic schemes for remotely preparing a four-qubit cluster-type entangled state. Int. J. Theor. Phys. 53, 2485–2491 (2014)

    MATH  Google Scholar 

  15. Wang, D., Hu, Y.-D., Wang, Z.-Q., Ye, L.: Efficient and faithful remote preparation of arbitrary three- and four-particle W-class entangled states. Quantum Inf. Process. 14(6), 2135–2151 (2015)

    ADS  MATH  Google Scholar 

  16. Wang, D., Huang, A.-J., Sun, W.-Y., Shi, J.-D., Ye, L.: Practical single-photon-assisted remote state Preparation with non-maximally entanglement. Quantum Inf. Process. 15(8), 3367–3381 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  17. Choudhury, B.S., Samanta, S.: Remote preparation of some three-particle entangled states under divided information. Int. J. Theor. Phys. 58, 83–91 (2019)

    MATH  Google Scholar 

  18. Choudhury, B.S., Samanta, S.: An optional remote state preparation protocol for a four-qubit entangled state. Quantum Inf. Process. 18, 118 (2019)

    ADS  MATH  Google Scholar 

  19. Jiao, X.F., Zhou, P., Lv, S.X., Wang, Z.Y.: Remote preparation for single-photon two-qubit hybrid state with hyperentanglement via linearoptical elements. Sci. Rep. 9, 4663 (2019)

    ADS  Google Scholar 

  20. Wang, Z.Y., Liu, Y.M., Zuo, X.Q., Zhang, Z.J.: Controlled Remote State Preparation. Commun. Theor. Phys. 52, 235–240 (2009)

    ADS  MATH  Google Scholar 

  21. Chen, X.B., Ma, S.Y., Su, Y., Zhang, R., Yang, Y.X.: Controlled remote state preparation of arbitrary two and three qubit states via the Brown state. Quantum Inf. Process. 11, 1653 (2012)

    ADS  MathSciNet  MATH  Google Scholar 

  22. Wang, C., Zeng, Z., Li, X.H.: Controlled remote state preparation via partially entangled quantum channel. Quantum Inf. Process. 14, 1077 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  23. Cao, T.B., Nguyen, B.A.: Deterministic controlled bidirectional remote state preparation. Adv. Nat. Sci.-Nanosci. 5, 015003 (2014)

    Google Scholar 

  24. Zhang, D., Zha, X., Duan, Y., Wei, Z.H.: Deterministic controlled bidirectional remote state preparation via a six-qubit maximally entangled state. Int. J. Theor. Phys. 55, 440–446 (2016)

    MATH  Google Scholar 

  25. Zhang, D., Zha, X., Duan, Y., Yang, Y.: Deterministic controlled bidirectional remote state preparation via a six-qubit entangled state. Quantum Inf. Process. 15, 2169–2179 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  26. Wang, X.Y., Mo, Z.W.: Bidirectional controlled joint remote state preparation via a seven-qubit entangled state. Int. J. Theor. Phys. 56, 1052–1058 (2017)

    MATH  Google Scholar 

  27. Chen, X.B., Sun, Y.R., Xu, G., Jia, H.Y., Qu, Z., Yang, Y.X.: Controlled bidirectional remote preparation of three-qubit state. Quantum Inf. Process. 16, 244 (2017)

    ADS  MATH  Google Scholar 

  28. Sharma, V., Shukla, C., Banerjee, S., Pathak, A.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. Quant. Inf. Process. 14, 3441–3464 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  29. Song, Y., Ni, J.L., Wang, Z.Y., Lu, Y., Han, L.F.: Deterministic bidirectional remote state preparation of a- and symmetric quantum states with a proper quantum channel. Int. J. Theor. Phys. 563175–3187 (2017)

  30. Ma, P.C., Chen, G.B., Li, X.W., Zhan, Y.B.: Asymmetric bidirectional controlled remote preparation of an arbitrary four-qubit cluster-type state and a single-qubit state. Quantum Inf. Process. 16308 (2017)

  31. Sun, Y.R., Chen, X.B., Xu, G., Yuan, K.G., Yang, Y.X.: Asymmetric controlled bidirectional remote preparation of two- and three-qubit equatorial state. Sci. Rep. 9, 2081 (2019)

    ADS  Google Scholar 

  32. Sang, Z.W.: Bidirectional controlled quantum information transmission by using a five-qubit cluster state. Int. J. Theor. Phys. 56, 3400–3404 (2017)

    MathSciNet  MATH  Google Scholar 

  33. Sang, M.H., Niel, L.P.: Asymmetric bidirectional controlled quantum information transmission via seven-particle entangled state. Int. J. Theor. Phys. 56, 3658 (2017)

    MathSciNet  Google Scholar 

  34. Wu, H., Zha, X.W., Yang, Y.Q.: Controlled bidirectional hybrid of remote state preparation and quantum teleportation via seven-qubit entangled state. Int. J. Theor. Phys. 57, 28 (2018)

    MATH  Google Scholar 

  35. Fang, S.H., Hiang, M.: a novel scheme for bidirectional and hybrid quantum information transmission via a seven-qubit state. Int. J. Theor. Phys. 57, 523–532 (2018)

    MathSciNet  MATH  Google Scholar 

  36. Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    ADS  MathSciNet  Google Scholar 

  37. Man, Z.X., Xia, Y.J., An, N.B.: Quantum secure direct communication by using GHZ states and entanglement swapping. J. Phys. B 39, 3855–3864 (2006)

    ADS  Google Scholar 

  38. Man, Z.X., Xia, Y.J., An, N.B.: Quantum state sharing of an arbitrary multiqubit state using nonmaximally entangled GHZ states. Eur. Phys. J. D 42, 333–340 (2007)

    ADS  MathSciNet  Google Scholar 

  39. Yang, K., Huang, L., Yang, W., Song, F.: Quantum teleportation via GHZ-like state. Int. J. Theor. Phys. 48, 516–521 (2009)

    MathSciNet  MATH  Google Scholar 

  40. Zhu, P.H.: Perfect teleportation of an arbitrary two-qubit state via GHZ-like states. Int. J. Theor. Phys. 53, 4095–4097 (2014)

    MATH  Google Scholar 

  41. Nandi, K., Mazumdar, C.: Quantum teleportation of a two-qubit state using GHZ-like state. Int. J. Theor. Phys. 53, 1322–1324 (2014)

    MATH  Google Scholar 

  42. Pati, A.K.: Quantum cobwebs: Universal entangling of quantum states. Pramana. J. Phys. 59, 221–228 (2002)

    ADS  Google Scholar 

  43. Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W-states. Phys. Rev. A 74, 062320 (2006)

    ADS  Google Scholar 

  44. Xiao, X.-Q., Liu, J.-M.: Remote preparation of a two-particle entangled state via two tripartite W entangled states. Int. J. Theor. Phys. 46, 2378–2383 (2007)

    MathSciNet  MATH  Google Scholar 

  45. An, N.B.: Joint remote state preparation via W and W-type states. Opt. Commun. 283, 4113–4117 (2010)

    ADS  Google Scholar 

  46. 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, 4483–4487 (2010)

    ADS  MATH  Google Scholar 

  47. Hou, K., Yu, J.-Y., Yan, F.: Deterministic remote preparation of a four-particle entangled W state. Int. J. Theor. Phys. 54, 3092–3102 (2015)

    MathSciNet  MATH  Google Scholar 

  48. Zhan, H.T., Yu, X.T., Xiong, P.Y., Zhang, Z.C.: Multi-hop teleportation based on W state and EPR pairs. Chin. Phys. B 25, 050305 (2016)

    Google Scholar 

  49. Toffoli, T.: Reversible computing. In: de Bakker, J, van Leeuwen, J (eds.) Automata, Languages and Programming. ICALP Lecture Notes in Computer Science, p 85. Springer, Berlin (1980)

  50. Nie, Y.-Y., Sang, M.-H.: Asymmetric bidirectional controlled teleportation via seven-photon entangled state. Int. J. Theor. Phys. 56, 3452–3454 (2017)

    MathSciNet  MATH  Google Scholar 

  51. Choudhury, B.S., Samanta, S.: Asymmetric bidirectional \( 3\leftrightarrow 2\) qubit teleportation protocol between Alice and Bob via 9-qubit cluster state. Int. J. Theor. Phys. 56, 3285–3296 (2017)

    MATH  Google Scholar 

  52. Jain, S., Muralidharan, S., Panigrahi, P.K.: Secure quantum conversation through non-destructive discrimination of highly entangled multipartite states. Europhys. Lett. 87, 60008 (2009)

    ADS  Google Scholar 

  53. Banerjee, A., Shukla, C., Thapliyal, K., Pathak, A., Panigrahi, P.K.: Asymmetric quantum dialogue in noisy environment. Quantum Inf. Process. 16(2), 49 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  54. Yuan, H., Liu, Y.M., Zhang, W., Zhang, Z.J.: Optimizing resource consumption, operation complexity and efficiency in quantum-state sharing. J. Phys. B: At. Mol. Opt. Phys. 41, 145506 (2008)

    ADS  Google Scholar 

  55. Shi, R., Huang, L., Yang, W.: Multi-party quantum state sharing of an arbitrary twoqubit state with Bell states. Quantum Inf. Process. 10, 231–239 (2011)

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

In this work, NBA is supported by the Foundation for Science and Technology Development (NAFOSTED) of Vietnam under project no. 103.01-2019.313, while BSC and SS by the University Grants Commission of India. The valuable suggestions of the reviewers are gratefully acknowledged.

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Authors and Affiliations

  1. Thang Long Institute of Mathematics and Applied Sciences Thang Long University, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam

    Nguyen Ba An

  2. Center for Theoretical Physics, Institute of Physics Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Nguyen Ba An

  3. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, West Bengal, India

    Binayak S. Choudhury & Soumen Samanta

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  1. Nguyen Ba An
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Correspondence to Soumen Samanta.

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An, N.B., Choudhury, B.S. & Samanta, S. Two-Way Remote Preparations of Inequivalent Quantum States Under a Common Control. Int J Theor Phys 60, 47–62 (2021). https://doi.org/10.1007/s10773-020-04657-0

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