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Hierarchical Quantum Network using Hybrid Entanglement

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Abstract

The advent of a new kind of entangled state known as hybrid entangled state, i.e., entanglement between different degrees of freedom, makes it possible to perform various quantum computational and communication tasks with lesser amount of resources. Here, we aim to exploit the advantage of these entangled states in communication over quantum networks. Unfortunately, the entanglement shared over the network deteriorates due to its unavoidable interaction with surroundings. Thus, an entanglement concentration protocol is proposed to obtain a maximally entangled hybrid Omega-type state from the corresponding non-maximally entangled states. The advantage of the proposed entanglement concentration protocol is that it is feasible to implement this protocol with linear optical components and present technology. The corresponding linear optical quantum circuit is provided for experimental realizations, while the success probability of the concentration protocol is also reported. Thereafter, we propose an application of maximally entangled hybrid state in the hierarchical quantum teleportation network by performing information splitting using Omega-type state, which is also the first hierarchical quantum communication scheme in the hybrid domain so far. The present hybrid entangled state has advantage in circumventing Pauli operations on the coherent state by polarization rotation of single qubit, which can be performed with lesser errors.

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References

  1. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  2. Menicucci, N.C., Loock, P.V., Gu, M., Weedbrook, C., Ralph, T.C., Nielsen, M.A.: Universal quantum computation with continuous-variable cluster states. Phys. Rev. Lett. 97, 110501 (2006)

    Article  ADS  Google Scholar 

  3. Bennett, C.H., Brassard, G., Crepeau, C., et al.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Ekert, A.K.: Quantum cryptography based on Bell’s Theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Shukla, C., Alam, N., Pathak, A.: Protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf. Process. 13, 2391 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Shukla, C., Thapliyal, K., Pathak, A.: Semi-quantum communication: protocols for key agreement, controlled secure direct communication and dialogue. Quantum Inf. Process. 16, 295 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Long, G.-L., Deng, F.-G., Wang, C., Li, X.-H., Wen, K., Wang, W.-Y.: Quantum secure direct communication and deterministic secure quantum communication. Front. Phys. China 2, 251 (2007)

    Article  ADS  Google Scholar 

  10. Shukla, C., Banerjee, A., Pathak, A., Srikanth, R.: Secure quantum communication with orthogonal states. Int. J. Quantum Inf. 14, 1640021 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kimble, H.J.: The quantum internet. Nature 453, 1023–1030 (2008)

    Article  ADS  Google Scholar 

  12. Pirandola, S.: End-to-end capacities of a quantum communication network. Comm. Phys. 2, 51 (2019)

    Article  ADS  Google Scholar 

  13. Morin, O., Huang, K., Liu, J., Jeannic, H.L., Fabre, C., Laurat, J.: Remote creation of hybrid entanglement between particle-like and wave-like optical qubits. Nat. Photon. 8, 570–574 (2014)

    Article  ADS  Google Scholar 

  14. Cao, T.B., Nguyen, B.A.: Hierarchically controlling quantum teleportations. Quantum Inf. Process. 18, 245 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  15. Li, W.-L., Li, C.-F., Guo, G.-C.: Probabilistic teleportation and entanglement Matching. Phys. Rev. A 61, 034301 (2000)

    Article  ADS  Google Scholar 

  16. Shukla, C., Thapliyal, K., Pathak, A.: Hierarchical joint remote state preparation in noisy environment. Quantum Inf. Process. 16, 205 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Pathak, A.: Elements of Quantum Computation and Quantum Communication. CRC Press, Boca Raton (2013)

    Book  MATH  Google Scholar 

  18. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996)

    Article  ADS  Google Scholar 

  19. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., et al.: Purification of noisy entanglement and faithful teleportation via noisy channel. Phys. Rev. Lett. 76, 722–725 (1996)

    Article  ADS  Google Scholar 

  20. Bose, S., Vedral, V., Knight, P.L.: Purification via entanglement swapping and conserved entanglement. Phys. Rev. A 60, 194–197 (1999)

    Article  ADS  Google Scholar 

  21. Zhao, Z., Pan, J.-W., Zhan, M.S.: Practical scheme for entanglement concentration. Phys. Rev. A 64, 014301 (2001)

    Article  ADS  Google Scholar 

  22. Sheng, Y.-B., Zhou, L., Zhao, S.-M., Zheng, B.-Y.: Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85, 012307 (2012)

    Article  ADS  Google Scholar 

  23. Shukla, C., Banerjee, A., Pathak, A.: Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and 9 families of 4-qubit entangled states. Quantum Inf. Process. 14, 2077 (2015)

    Article  ADS  MATH  Google Scholar 

  24. Liu, J., Zhou, L., Zhong, W., Sheng, Y.-B.: Logic Bell state concentration with parity check measurement. Front. Phys. 14, 21601 (2019)

    Article  ADS  Google Scholar 

  25. Wang, X., Hu, Z.-N.: Entanglement concentration for photon systems assisted with single photons. Optik. Int. J. Light Electr. Opt. 176, 143–151 (2019)

    Article  Google Scholar 

  26. Pan, J.-W., Simon, C., Brukner, C., Zeilinger, A.: Entanglement purification for quantum communication. Nature 410, 1067 (2001)

    Article  ADS  Google Scholar 

  27. Yamamoto, T., Koashi, M., Imoto, N.: Concentration and purification scheme for two partially entangled photon pairs. Phys. Rev. A 64, 012304 (2001)

    Article  ADS  Google Scholar 

  28. Zwerger, M., Briegel, H.J., Dur, W.: Universal and optimal error thresholds for measurement-based entanglement purification. Phys. Rev. Lett. 110, 260503 (2013)

    Article  ADS  Google Scholar 

  29. Zhou, L., Sheng, Y.-B.: Purification of logic-qubit entanglement. Sci. Rep. 6, 28813 (2016)

    Article  ADS  Google Scholar 

  30. Sanders, B.C.: Review of entangled coherent states. J. Phys. A Math. Theor. 45, 244002 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Yukawa, M., Ukai, R., van Loock, P., Furusawa, A.: Experimental generation of four-mode continuous-variable cluster states. Phys. Rev. A 78, 012301 (2008)

    Article  ADS  MATH  Google Scholar 

  32. Su, X., Tan, A., Jia, X., Zhang, J., Xie, C., Peng, K.: Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables. Phys. Rev. Lett. 98, 070502 (2007)

    Article  ADS  Google Scholar 

  33. Luiz, F.S., Rigolin, G.: Teleportation-based continuous variable quantum cryptography. Quantum Inf. Process. 16, 58 (2017)

    Article  ADS  MATH  Google Scholar 

  34. Weedbrook, C., Pirandola, S., Garcia-Patron, R., Cerf, N.J., et al.: Gaussian quantum information. Rev. Mod. Phys. 84, 621 (2012)

    Article  ADS  Google Scholar 

  35. An, N.B.: Optimal processing of quantum information via W-type entangled coherent states. Phys. Rev. A 69, 022315 (2004)

    Article  ADS  Google Scholar 

  36. Sheng, Y.-B., Liu, J., Zhao, S.-Y., Wang, L., Zhou, L.: Entanglement concentration for W-type entangled coherent states. Chin. Phys. B 23, 080305 (2014)

    Article  ADS  Google Scholar 

  37. Sisodia, M., Shukla, C., Long, G.L.: Linear optics-based entanglement concentration protocols for cluster-type entangled coherent state. Quantum Inf. Process. 18, 253 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  38. Zhao, Z., Yang, T., Chen, Y.-A., Zhang, A.-N., Pan, J.-W.: Experimental realization of entanglement concentration and a quantum repeater. Phys. Rev. Lett. 90, 207901 (2003)

    Article  ADS  Google Scholar 

  39. Chen, L.-K., Yong, H.-L., Xu, P., et al.: Experimental nested purification for a linear optical quantum repeater. Nat. Photon. 11, 695–699 (2017)

    Article  ADS  Google Scholar 

  40. van Loock, P., Ladd, T.D., Sanaka, K., Yamaguchi, F., Nemoto, K., Munro, W.J., Yamamoto, Y.: Hybrid quantum repeater using bright coherent light. Phys. Rev. Lett. 96, 240501 (2006)

    Article  Google Scholar 

  41. Jeong, H., Zavatta, A., Kang, M., Lee, S.-W., Costanzo, L.S., Grandi, S., Ralph, T.C., Bellini, M.: Generation of hybrid entanglement of light. Nat. Photon. 8, 564–569 (2014)

    Article  ADS  Google Scholar 

  42. Kwon, H., Jeong, H.: Generation of hybrid entanglement between a single-photon polarization qubit and a coherent state. Phys. Rev. A 91, 012340 (2015)

    Article  ADS  Google Scholar 

  43. Podoshvedov, S.A., Nguyen, B.A.: Designs of interactions between discrete- and continuous-variable states for generation of hybrid entanglement. Quantum Inf. Process. 18, 68 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. 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)

    Article  ADS  Google Scholar 

  45. Brask, J.B., Rigas, I., Polzik, E.S., Andersen, U.L., Sørensen, A.S.: Hybrid long-distance entanglement distribution protocol. Phys. Rev. Lett. 105, 160501 (2010)

    Article  ADS  Google Scholar 

  46. Andersen, U.L., Neergaard-Nielsen, J.S., van Loock, P., Furusawa, A.: Hybrid discrete- and continuous-variable quantum information. Nat. Phys. 11, 713–719 (2015)

    Article  Google Scholar 

  47. Ulanov, A.E., Sychev, D., Pushkina, A.A., Fedorov, I.A., Lvovsky, A.I.: Quantum teleportation between discrete and continuous encodings of an optical qubit. Phys. Rev. Lett. 118, 160501 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  48. Sychev, D.V., Ulanov, A.E., Tiunov, E.S., Pushkina, A.A., Kuzhamuratov, A., Novikov, V., Lvovsky, A.I.: Entanglement and teleportation between polarization and wave-like encodings of an optical qubit. Nat. Comm. 9, 3672 (2018)

    Article  ADS  Google Scholar 

  49. Jeannic, H.L., Cavailles, A., Raskop, J., Huang, K., Laurat, J.: Remote preparation of continuous-variable qubits using loss-tolerant hybrid entanglement of light. Optica 5, 1012–1015 (2018)

    Article  ADS  Google Scholar 

  50. Podoshvedov, S.A.: Efficient quantum teleportation of unknown qubit based on DV-CV interaction mechanism. Entropy 21, 150 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  51. Guccione, G., Cavaill\(\grave{e}\)s, A., Darras, T., Jeannic, H.L, Raskop, J., Huang, K., Laurat, J.: Quantum communication protocols based on hybrid entanglement of light. in Quantum Information and Measurement (QIM) V: Quantum Technologies, OSA Technical Digest (Optical Society of America, 2019), paper F5A.3

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

    Article  ADS  Google Scholar 

  53. Sheng, Y.-B., Zhou, L., Long, G.-L.: Hybrid entanglement purification for quantum repeaters. Phys. Rev. A 88, 022302 (2013)

    Article  ADS  Google Scholar 

  54. Guo, R., Zhou, L., Gu, S.-P., Wang, X.-F., Sheng, Y.-B.: Hybrid entanglement concentration assisted with single coherent state. Chin. Phys. B 25, 030302 (2016)

    Article  Google Scholar 

  55. Wang, R., Wang, T.-J., Wang, C.: Entanglement purification and concentration based on hybrid spin entangled states of separate nitrogen-vacancy centers. EPL 126, 40006 (2019)

    Article  ADS  Google Scholar 

  56. Shukla, C., Kothari, V., Banerjee, A., Pathak, A.: On the group-theoretic structure of a class of quantum dialogue protocols. Phys. Lett. A 377, 518 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. Shukla, C., Pathak, A.: Hierarchical quantum communication. Phys. Lett. A 377, 1337–1344 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  58. Mishra, S., Shukla, C., Pathak, A., Srikanth, R., Venugopalan, A.: An integrated hierarchical dynamic quantum secret sharing protocol. Int. J. Theor. Phys. 54, 3143–3154 (2015)

    Article  MATH  Google Scholar 

  59. Omkar, S., Teo, Y.S., Jeong, H.: Resource-efficient topological fault-tolerant quantum computation with hybrid entanglement of light. Phys. Rev. Lett. 125, 060501 (2020)

    Article  ADS  Google Scholar 

  60. Verstraete, F., Dehaene, J., Moor, B.D., Verschelde, H.: Four qubits can be entangled in nine different ways. Phys. Rev. A 65, 052112 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  61. Pradhan, B., Agrawal, P., Pati, A.K.: Teleportation and superdense coding with genuine quadripartite entangled states. arXiv:0705.1917v1 (2007)

  62. Nielsen, M.A.: Conditions for a class of entanglement transformations. Phys. Rev. Lett. 83, 436 (1999)

    Article  ADS  Google Scholar 

  63. Chen, P.-X., Zhu, S.-Y., Guo, G.-C.: General form of genuine multipartite entanglement quantum channels for teleportation. Phy. Rev. A 74, 032324 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  65. Banerjee, A., Thapliyal, K., Shukla, C., Pathak, A.: Quantum conference. Quantum Inf. Process. 17, 161 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

KT acknowledges the financial support from the Operational Programme Research, Development and Education—European Regional Development Fund Project No. CZ.02.1.01/0.0/0.0/16_019/0000754 of the Ministry of Education, Youth and Sports of the Czech Republic. PM thanks Peng Cheng Laboratory (PCL), Shenzhen, China, for the hospitality provided during her visit. The authors also thank Prof. Anirban Pathak for his interest in the work and helpful suggestions.

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Authors and Affiliations

  1. Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen, 518055, People’s Republic of China

    Chitra Shukla

  2. Indian Institute of Technology Jodhpur, Jodhpur, 342037, India

    Priya Malpani

  3. RCPTM, Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Science of the Czech Republic, Faculty of Science, Palacky University, 17. listopadu 12, Olomouc, 771 46, Czech Republic

    Kishore Thapliyal

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  1. Chitra Shukla
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Shukla, C., Malpani, P. & Thapliyal, K. Hierarchical Quantum Network using Hybrid Entanglement. Quantum Inf Process 20, 121 (2021). https://doi.org/10.1007/s11128-021-03057-5

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