Abstract
In this paper, we propose an efficient scheme to fast generate three-particle Greenberger–Horne–Zeilinger (GHZ) state based on quantum Zeno dynamics and designing the evolution operators with Rydberg superatom. In the present scheme, the quantum information is encoded in the collective states of superatom which contains n individual four-level inverted Y-type Rydberg atoms, and the Rabi frequency can be fitted to a Gaussian function, which favors experimental feasibility. In addition, the influence of various decoherence factors such as atomic spontaneous emission, cavity decay and fiber leakage is also considered. The numerical simulation result shows that the present scheme is robust against decoherence and operational imperfection. At last, we generalize this scheme to the generation of N-particle GHZ state.







Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
References
Bennett, C.H., Brassard, G., Crépeau, 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)
Pirandola, S., Eisert, J., Weedbrook, C., Furusawa, A., Braunstein, S.L.: Advances in quantum teleportation. Nat. Photonics 9, 641–652 (2015)
Barenco, A., Ekert, A.K.: Dense coding based on quantum entanglement. J. Mod. Opt. 42, 1253–1259 (1995)
Hao, J.C., Li, C.F., Guo, G.C.: Controlled dense coding using the Greenberger-Horne-Zeilinger state. Phys. Rev. A 63, 054301 (2001)
Jing, J., Zhang, J., Yan, Y., Zhao, F., Xie, C., Peng, K.: Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables. Phys. Rev. Lett. 90, 167903 (2003)
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)
Pirandola, S., Andersen, U.L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C., Ottaviani, C.: Advances in quantum cryptography. Adv. Opt. Photonics 12, 1012–1236 (2020)
Portmann, C., Renner, R.: Security in quantum cryptography. Rev. Mod. Phys. 94, 025008 (2022)
DiVincenzo, D.P.: Quantum computation. Science 270, 255–261 (1995)
Briegel, H.J., Browne, D.E., Dür, W., Raussendorf, R., Van den Nest, M.: Measurement-based quantum computation. Nat. Phys. 5, 19–26 (2009)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41, 303–332 (1999)
Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bell’s theorem without inequalities. Am. J. Phys. 58, 1131–1143 (1990)
Bouwmeester, D., Pan, J.W., Daniell, M., Weinfurter, H., Zeilinger, A.: Observation of three-photon Greenberger-Horne-Zeilinger entanglement. Phys. Rev. Lett. 82, 1345 (1999)
Hao, J.C., Li, C.F., Guo, G.C.: Controlled dense coding using the Greenberger-Horne-Zeilinger state. Phys. Rev. A 63, 054301 (2001)
Qin, H., Dai, Y.: Dynamic quantum secret sharing by using D-dimensional GHZ state. Quantum Inf. Process. 16, 1–13 (2017)
Bastin, T., Thiel, C., Von Zanthier, J., Lamata, L., Solano, E., Agarwal, G.S.: Operational determination of multiqubit entanglement classes via tuning of local operations. Phys. Rev. Lett. 102, 053601 (2009)
Barrett, S.D., Kok, P.: Efficient high-fidelity quantum computation using matter qubits and linear optics. Phys. Rev. A 71, 060310 (2005)
Ji, Y.Q., Jin, Z., Zhu, A.D., Wang, H.F., Zhang, S.: Concentration of multi-photon entanglement with linear optics assisted by quantum nondemolition detection. JOSA B 31, 994–999 (2014)
Gerry, C.C.: Proposal for a mesoscopic cavity QED realization of the Greenberger-Horne-Zeilinger state. Phys. Rev. A 54, R2529 (1996)
Guo, G.P., Li, C.F., Li, J., Guo, G.C.: Scheme for the preparation of multiparticle entanglement in cavity QED. Phys. Rev. A 65, 042102 (2002)
Ye, L., Yu, L.B., Guo, G.C.: Generation of entangled states in cavity QED. Phys. Rev. A 72, 034304 (2005)
Yang, Z.B.: Generation of four-particle GHZ states in bimodal cavity QED. Chin. Phys. 16, 1963 (2007)
Chen, Y.H., Xia, Y., Song, J., Chen, Q.Q.: Shortcuts to adiabatic passage for fast generation of Greenberger-Horne-Zeilinger states by transitionless quantum driving. Sci. Rep. 5, 15616 (2015)
Ji, Y.Q., Li, H., Liu, Y.L., Zhang, D.W., Zhou, X.J., Xiao, R.J., Dong, L., Xiu, X.M.: Preparation of entangled states in multiple cavities. Laser Phys. Lett. 17, 085202 (2020)
Wei, L., Liu, Y., Nori, F.: Generation and control of Greenberger-Horne-Zeilinger entanglement in superconducting circuits. Phys. Rev. Lett. 96, 246803 (2006)
DiCarlo, L., Reed, M.D., Sun, L., Johnson, B.R., Chow, J.M., Gambetta, J.M., Frunzio, L., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010)
Song, C., Xu, K., Liu, W., Yang, C., Zheng, S.B., Deng, H., Xie, Q., Huang, K., Guo, Q., Zhang, L., Zhang, P., Xu, D., Zheng, D., Zhu, X., Wang, H., Chen, Y.A., Lu, C.Y., Han, S., Pan, J.W.: 10-qubit entanglement and parallel logic operations with a superconducting circuit. Phys. Rev. Lett. 119, 180511 (2017)
Feng, W., Zhang, G.Q., Su, Q.P., Zhang, J.X., Yang, C.P.: Generation of Greenberger-Horne-Zeilinger states on two-dimensional superconducting-qubit lattices via parallel multiqubit-gate operations. Phys. Rev. Appl 18, 064036 (2022)
Yu, W.R., Ji, X.: Fast preparing W state via a chosen path shortcut in circuit QED. Quantum Inf. Process. 18, 1–12 (2019)
Chen, X., Ruschhaupt, A., Schmidt, S., del Campo, A., Guéry-Odelin, D., Muga, J.G.: Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity. Phys. Rev. Lett. 104, 063002 (2010)
Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.: Shortcut to adiabatic passage in two-and three-level atoms. Phys. Rev. Lett. 105, 123003 (2010)
Guéry-Odelin, D., Ruschhaupt, A., Kiely, A., Torrontegui, E., Martínez-Garaot, S., Muga, J.G.: Shortcuts to adiabaticity: concepts, methods, and applications. Rev. Mod. Phys. 91, 045001 (2019)
Lewis, H.R., Jr., Riesenfeld, W.: An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field. J. Math. Phys. 10, 1458–1473 (1969)
Chen, Y.H., Xia, Y., Chen, Q.Q., Song, J.: Fast and noise-resistant implementation of quantum phase gates and creation of quantum entangled states. Phys. Rev. A 91, 012325 (2015)
Wu, J.L., Ji, X., Zhang, S.: Fast generations of tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving. Sci. Rep. 6, 33669 (2016)
Berry, M.V.: Transitionless quantum driving. J. Phys. A: Math. Theor. 42, 365303 (2009)
Ji, Y.Q., Liu, Y.L., Zhou, S.J., Xiu, X.M., Dong, L., Dong, H.K., Gao, Y.J., Yi, X.X.: Fast conversion of dicke states \(|{D_n^{(2)}}\rangle \) to \(|{D_{n+1}^{(2)}}\rangle \) by transitionless quantum driving. Phys. Rev. A 99, 023808 (2019)
Lim, R., Berry, M.: Superadiabatic tracking of quantum evolution. J. Phys. A: Math. Gen. 24, 3255 (1991)
Ibáñez, S., Chen, X., Muga, J.: Improving shortcuts to adiabaticity by iterative interaction pictures. Phys. Rev. A 87, 043402 (2013)
Wu, J.L., Su, S.L., Ji, X., Zhang, S.: Superadiabatic scheme for optimizing the fast generation of tree-type 3d entanglement. Ann. Phys. 386, 34–43 (2017)
Song, X.K., Ai, Q., Qiu, J., Deng, F.G.: Physically feasible three-level transitionless quantum driving with multiple schrödinger dynamics. Phys. Rev. A 93, 052324 (2016)
Baksic, A., Ribeiro, H., Clerk, A.A.: Speeding up adiabatic quantum state transfer by using dressed states. Phys. Rev. Lett. 116, 230503 (2016)
Wu, J.L., Ji, X., Zhang, S.: Fast adiabatic quantum state transfer and entanglement generation between two atoms via dressed states. Sci. Rep. 7, 46255 (2017)
Kang, Y.H., Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Fast preparation of W states with superconducting quantum interference devices by using dressed states. Phys. Rev. A 94, 052311 (2016)
Kang, Y.H., Chen, Y.H., Wu, Q.C., Huang, B.H., Xia, Y., Song, J.: Reverse engineering of a hamiltonian by designing the evolution operators. Sci. Rep. 6, 30151 (2016)
Stiesdal, N., Busche, H., Kumlin, J., Kleinbeck, K., Büchler, H.P., Hofferberth, S.: Observation of collective decay dynamics of a single rydberg superatom. Phys. Rev. Res. 2, 043339 (2020)
Zeiher, J., Schauß, P., Hild, S., Macrì, T., Bloch, I., Gross, C.: Microscopic characterization of scalable coherent rydberg superatoms. Phys. Rev. X 5, 031015 (2015)
Stiesdal, N., Kumlin, J., Kleinbeck, K., Lunt, P., Braun, C., Paris-Mandoki, A., Tresp, C., Büchler, H.P., Hofferberth, S.: Observation of three-body correlations for photons coupled to a rydberg superatom. Phys. Rev. Lett. 121, 103601 (2018)
Pritchard, J.D., Maxwell, D., Gauguet, A., Weatherill, K.J., Jones, M., Adams, C.S.: Cooperative atom-light interaction in a blockaded Rydberg ensemble. Phys. Rev. Lett. 105, 193603 (2010)
Colombe, Y., Steinmetz, T., Dubois, G., Linke, F., Hunger, D., Reichel, J.: Strong atom-field coupling for bose-einstein condensates in an optical cavity on a chip. Nature 450, 272–276 (2007)
Zhang, W.Y., Wang, C.Q., Ji, Y.Q., Shao, Q.P., Wang, J.P., Wang, J., Yang, L.P., Dong, L., Xiu, X.M.: Fast preparation of W states by designing the evolution operators with Rydberg superatom. Adv. Quantum Technol. 7, 2300140 (2024)
Shao, X.-Q., Su, S.-L., Li, L., Nath, R., Wu, J.-H., Li, W.: Rydberg superatoms: an artificial quantum system for quantum information processing and quantum optics. Appl. Phys. Rev. 11, 031320 (2024)
Saffman, M., Walker, T.G., Mølmer, K.: Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313 (2010)
Ji, Y.Q., Liu, Y.L., Li, H., Zhou, X.J., Xiao, R.J., Dong, L., Xiu, X.M.: Fast preparation of Bell state and W state with Rydberg superatom. Quantum Inf. Process. 19, 1–12 (2020)
Xing, T., Zhao, P., Tong, D.: Realization of nonadiabatic holonomic multiqubit controlled gates with rydberg atoms. Phys. Rev. A 104, 012618 (2021)
Wu, J.L., Wang, Y., Han, J.X., Su, S.L., Xia, Y., Song, J., Jiang, Y.: Fast and robust multiqubit gates on Rydberg atoms by periodic pulse engineering. Adv. Quantum Technol. 5, 2200042 (2022)
Ji, Y.Q., Dai, C.M., Shao, X.Q., Yi, X.X.: Entangled state fusion with Rydberg atoms. Quantum Inf. Process. 16, 1–14 (2017)
Zhao, P., Cui, X.-D., Xu, G., Sjöqvist, E., Tong, D.: Rydberg-atom-based scheme of nonadiabatic geometric quantum computation. Phys. Rev. A 96, 052316 (2017)
Paris-Mandoki, A., Braun, C., Kumlin, J., Tresp, C., Mirgorodskiy, I., Christaller, F., Büchler, H.P., Hofferberth, S.: Free-space quantum electrodynamics with a single Rydberg superatom. Phys. Rev. X 7, 041010 (2017)
Zhao, P., Wu, X., Xing, T., Xu, G., Tong, D.: Nonadiabatic holonomic quantum computation with Rydberg superatoms. Phys. Rev. A 98, 032313 (2018)
Liu, Y.L., Ji, Y.Q., Han, X., Cui, W.X., Zhang, S., Wang, H.F.: Fast conversion of three-particle Dicke states to four-particle Dicke states with Rydberg superatoms. Adv. Quantum Technol. 6, 2200173 (2023)
Facchi, P., Pascazio, S.: Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002)
Facchi, P., Pascazio, S.: Quantum Zeno dynamics: mathematical and physical aspects. J. Phys. A: Math. Theor. 41, 493001 (2008)
Schäfer, F., Herrera, I., Cherukattil, S., Lovecchio, C., Cataliotti, F.S., Caruso, F., Smerzi, A.: Experimental realization of quantum Zeno dynamics. Nat. Commun. 5, 3194 (2014)
Ji, Y.Q., Shao, X.Q., Yi, X.X.: Fusing atomic W states via quantum Zeno dynamics. Sci. Rep. 7, 1378 (2017)
Farhi, E., Goldstone, J., Gutmann, S. , Sipser, M.: Quantum computation by adiabatic evolution. arXiv preprint quant-ph/0001106 (2000)
Roland, J., Cerf, N.J.: Quantum search by local adiabatic evolution. Phys. Rev. A 65, 042308 (2002)
Liu, S., Li, J., Yu, R., Wu, Y.: Achieving three-dimensional entanglement between two spatially separated atoms by using the quantum zeno effect. Phys. Rev. A 87, 062316 (2013)
Shan, W.-J., Xia, Y., Chen, Y.-H., Song, J.: Fast generation of n-atom greenberger-horne-zeilinger state in separate coupled cavities via transitionless quantum driving. Quantum Inf. Process. 15, 2359–2376 (2016)
Shao, X.-Q., Zheng, T.-Y., Feng, X.-L., Oh, C., Zhang, S.: One-step implementation of the genuine fredkin gate in high-q coupled three-cavity arrays. JOSA B 31, 697–703 (2014)
Yang, L., Wang, J., Ji, Y., Wang, J., Zhang, Z., Liu, Y., Dong, L., Xiu, X.: Fast generation of ghz state with rydberg superatom by transitionless quantum driving. Eur. Phys. J. Plus 139, 1–12 (2024)
Chen, Z., Chen, Y.-H., Xia, Y., Song, J., Huang, B.-H.: Fast generation of three-atom singlet state by transitionless quantum driving. Sci. Rep. 6, 22202 (2016)
Paris-Mandoki, A., Braun, C., Kumlin, J., Tresp, C., Mirgorodskiy, I., Christaller, F., Büchler, H.P., Hofferberth, S.: Free-space quantum electrodynamics with a single Rydberg superatom. Phys. Rev. X. 4, 041010 (2017)
Acknowledgements
This work was supported by the Program of the Educational Office of LiaoNing Province of China (Grant Nos. LJ212410167045, LJKZ1015, LJ2020005, LJKZZ20220120), the Natural Science Foundation of LiaoNing Province (Grant Nos. 2020-BS-234, 2021-MS-317, 2022-MS-372), the Program of Liaoning BaiQianWan Talents Program (Grant No. 2021921096).
Author information
Authors and Affiliations
Contributions
J. P. Wang and Y. Q. Ji wrote the main manuscript text, J. P. Wang prepared figures 1-7. All authors reviewed the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wang, J.P., Yang, L.P., Ji, Y.Q. et al. Fast generation of GHZ state by designing the evolution operators with Rydberg superatom. Quantum Inf Process 23, 377 (2024). https://doi.org/10.1007/s11128-024-04587-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-024-04587-4