Skip to main content
Log in

Generation of a hybrid W entangled state of three photonic qubits with different encodings

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The W-type entangled states are very useful in quantum computing and quantum communication. Many works have been devoted to preparing non-hybrid W states (i.e., all qubits with the same encoding) in various physical systems. On the other hand, hybrid W entangled states are key ingredients for hybrid quantum computing and quantum communication. In this work, we propose to create a hybrid W entangled state of three photonic qubits each with a different encoding. The hybrid W state is prepared by employing three microwave cavities coupled to a superconducting flux qutrit (i.e., a three-level quantum system). This proposal requires only a single qutrit to couple the three cavities, thus the system architecture is greatly simplified. Since there is no need of making any measurement, the W state is created deterministically. As an example, our numerical simulation demonstrates that within current experimental technology, the proposed hybrid W state can be created with a high fidelity. This proposal is universal and can be applied to create the proposed hybrid W state, by using three microwave or optical cavities coupled to a three-level natural or artificial atom.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: No data are used to produce any result in the paper. All the figures in the manuscript are produced using the equations derived in the manuscript.]

References

  1. Ekert, A., Jozsa, R.: Quantum computation and Shor’s factoring algorithm. Rev. Mod. Phys. 68(3), 733–753 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  2. 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(13), 1895–1899 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  3. Jennewein, T., Simon, C., Weihs, G., Weinfurter, H., Zeilinger, A.: Quantum cryptography with entangled photons. Phys. Rev. Lett. 84(20), 4729–4732 (2000)

    Article  ADS  Google Scholar 

  4. Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bell’s theorem without inequalities. Am. J. Phys. 58(12), 1131–1143 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  5. Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62(6), 062314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  6. Gorbachev, V.N., Trubilko, A.I., Rodichkina, A.A., Zhiliba, A.I.: Can the states of the W-class be suitable for teleportation. Phys. Lett. A 314(4), 267–271 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  7. Joo, J., Park, Y.J., Oh, S., Kim, J.: Quantum teleportation via a W state. New J. Phys. 5, 136 (2003)

    Article  ADS  Google Scholar 

  8. Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74(6), 062320 (2006)

    Article  ADS  Google Scholar 

  9. Joo, J., Lee, J., Jang, J., Park, Y.J.: Quantum secure communication with W states. J. Korean Phys. Soc. 46(4), 763–768 (2005)

    Google Scholar 

  10. Cao, H.J., Song, H.S.: Quantum secure direct communication with W state. Chin. Phys. Lett. 23(2), 290–292 (2006)

    Article  ADS  Google Scholar 

  11. Jones, D., Rahmani, A.: Optimal preparation of the maximally entangled W state of three superconducting gmon qubits. arXiv:1909.09289

  12. Zou, X.B., Pahlke, K., Mathis, W.: Generation of an entangled four-photon W state. Phys. Rev. A 66(4), 044302 (2002)

    Article  ADS  Google Scholar 

  13. Yamamoto, T., Tamaki, K., Koashi, M., Imoto, N.: Polarization-entangled W state using parametric down conversion. Phys. Rev. A 66(6), 064301 (2002)

    Article  ADS  Google Scholar 

  14. Wang, X., Feng, M., Sanders, B.C.: Multipartite entangled states in coupled quantum dots and cavity QED. Phys. Rev. A 67(2), 022302 (2003)

    Article  ADS  Google Scholar 

  15. Xue, P., Guo, G.C.: Scheme for preparation of mulipartite entanglement of atomic ensembles. Phys. Rev. A 67(3), 034302 (2003)

    Article  ADS  Google Scholar 

  16. Biswas, A., Agarwal, G.S.: Preparation of W, GHZ, and two-qutrit states using bimodal cavities. J. Mod. Opt. 51(11), 1627–1636 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  17. Song, K.H., Zhou, Z.W., Guo, G.C.: Quantum logic gate operation and entanglement with superconducting quantum interference devices in a cavity via a Raman transition. Phys. Rev. A 71(5), 052310 (2005)

    Article  ADS  Google Scholar 

  18. Zhang, X.L., Gao, K.L., Feng, M.: Preparation of cluster states and W states with superconducting quantum interference-device qubits in cavity QED. Phys. Rev. A 74(2), 024303 (2006)

    Article  ADS  Google Scholar 

  19. Deng, Z.J., Gao, K.L., Feng, M.: Generation of N-qubit W states with rf SQUID qubits by adiabatic passage. Phys. Rev. A 74(6), 064303 (2006)

    Article  ADS  Google Scholar 

  20. Jeong, H., An, N.B.: Greenberger–Horne–Zeilinger-type and W-type entangled coherent states: generation and Bell-type inequality tests without photon counting. Phys. Rev. A 74(2), 022104 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  21. Li, G.X.: Generation of pure multipartite entangled vibrational states for ions trapped in a cavity. Phys. Rev. A 74(5), 055801 (2006)

    Article  ADS  Google Scholar 

  22. Yuan, C.H., Ou, Y.C., Zhang, Z.M.: A scheme for preparation of W-type entangled coherent state of three-cavity fields. Chin. Phys. Lett. 23(7), 1695–1697 (2006)

    Article  ADS  Google Scholar 

  23. Chen, M.F., Jiang, X.P.: Generation of W-type entangled coherent states of three-cavity fields by a driving classical field. Commun. Theor. Phys. 46(2), 303–305 (2006)

    Article  ADS  Google Scholar 

  24. Guo, Y., Kuang, L.M.: Near-deterministic generation of four-mode W-type entangled coherent states. J. Phys. B At. Mol. Opt. Phys. 40(16), 3309–3318 (2007)

    Article  ADS  Google Scholar 

  25. Yu, C.S., Yi, X.X., Song, H.S., Mei, D.: Robust preparation of Greenberger–Horne–Zeilinger and W states of three distant atoms. Phys. Rev. A 75(4), 044301 (2007)

    Article  ADS  Google Scholar 

  26. Song, K.H., Xiang, S.H., Liu, Q., Lu, D.H.: Quantum computation and W-state generation using superconducting flux qubits coupled to a cavity without geometric and dynamical manipulation. Phys. Rev. A 75(3), 032347 (2007)

    Article  ADS  Google Scholar 

  27. Sharma, S.S., Almeida, E., Sharma, N.K.: Multipartite entanglement of three trapped ions in a cavity and W-state generation. J. Phys. B 41(16), 165503 (2008)

    Article  Google Scholar 

  28. Guo, Y., Deng, H.L.: Near-deterministic generation of three-mode W-type entangled coherent states in free-travelling optical fields. J. Phys. B At. Mol. Opt. Phys. 42(21), 215507 (2009)

    Article  ADS  Google Scholar 

  29. Gao, Y., Zhou, H., Zou, D., Peng, X., Du, J.: Preparation of Greenberger–Horne–Zeilinger and W states on a one-dimensional Ising chain by global control. Phys. Rev. A 87(3), 032335 (2013)

    Article  ADS  Google Scholar 

  30. Perez-Leija, A., Hernandez-Herrejon, J.C., Moya-Cessa, H.: Generating photon-encoded W states in multiport waveguide-array systems. Phys. Rev. A 87(1), 013842 (2013)

    Article  ADS  Google Scholar 

  31. Sweke, R., Sinayskiy, I., Petruccione, F.: Dissipative preparation of large W states in optical cavities. Phys. Rev. A 87(4), 042323 (2013)

    Article  ADS  Google Scholar 

  32. He, X.L., Su, Q.P., Zhang, F.Y., Yang, C.P.: Generating multipartite entangled states of qubits distributed in different cavities. Quantum Inf. Process. 13(6), 1381–1395 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  33. Zang, X.P., Yang, M., Ozaydin, F., Song, W., Cao, Z.L.: Generating multi-atom entangled W states via light-matter interface based fusion mechanism. Sci. Rep. 5(1), 16245 (2015)

    Article  ADS  Google Scholar 

  34. Menotti, M., Maccone, L., Sipe, J.E., Liscidini, M.: Generation of energy-entangled W states via parametric fluorescence in integrated devices. Phys. Rev. A 94(1), 013845 (2016)

    Article  ADS  Google Scholar 

  35. Liu, T., Su, Q.P., Xiong, S.J., Liu, J.M., Yang, C.P., Nori, F.: Generation of a macroscopic entangled coherent state using quantum memories in circuit QED. Sci. Rep. 6(1), 32004 (2016)

    Article  ADS  Google Scholar 

  36. Kim, Y.S., Cho, Y.W., Lim, H.T., Han, S.W.: Efficient generation of multipartite W state via quantum eraser. Phys. Rev. A 101(2), 022337 (2020)

    Article  ADS  Google Scholar 

  37. Zhang, Y., Liu, T., Yu, Y., Yang, C.P.: Preparation of entangled W states with cat-state qubits in circuit QED. Quantum Inf. Process. 19(8), 218 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  38. Cole, D.C., Wu, J.J., Erickson, S.D., Hou, P.Y., Wilson, A.C., Leibfried, D., Reiter, F.: Dissipative preparation of W states in trapped ion systems. New J. Phys. 23, 073001 (2021)

    Article  ADS  Google Scholar 

  39. Neeley, M., Bialczak, R.C., Lenander, M., Lucero, E., Mariantoni, M., O’Connell, A.D., Sank, D., Wang, H., Weides, M., Wenner, J., Yin, Y., Yamamoto, T., Cleland, A.N., Martinis, J.M.: Generation of three-qubit entangled states using superconducting phase qubits. Nature 467(7315), 570–573 (2010)

    Article  ADS  Google Scholar 

  40. Mlynek, J.A., Abdumalikov, A.A., Jr., Fink, J.M., Steffen, L., Baur, M., Lang, C., van Loo, A.F., Wallraff, A.: Demonstrating W-type entanglement of Dicke-states in resonant cavity quantum electrodynamics. Phys. Rev. A 86(5), 053838 (2012)

    Article  ADS  Google Scholar 

  41. Swain, M., Devrari, V., Rai, A., Behera, B.K., Panigrahi, P.K.: Generation of perfect W-state and demonstration of its application to quantum information splitting. arXiv:2006.01742

  42. Papp, S.B., Choi, K.S., Deng, H., Lougovski, P., van Enk, S.J., Kimble, H.J.: Characterization of multipartite entanglement for one photon shared among four optical modes. Science 324(5928), 764–768 (2009)

    Article  ADS  Google Scholar 

  43. Fang, B., Menotti, M., Liscidini, M., Sipe, J.E., Lorenz, V.O.: Three-photon discrete-energy-entangled w state in optical fiber. Phys. Rev. Lett. 123(7), 070508 (2019)

    Article  ADS  Google Scholar 

  44. Häffner, H., Hänsel, W., Roos, C.F., Benhelm, J., Chek-al-kar, D., Chwalla, M., Koärber, T., Rapol, U.D., Riebe, M., Schmidt, P.O., Becher, C., Gühne, O., Dür, W., Blatt, R.: Scalable multiparticle entanglement of trapped ions. Nature 438(7068), 643–646 (2005)

    Article  ADS  Google Scholar 

  45. Choi, K.S., Goban, A., Papp, S.B., van Enk, S.J., Kimble, H.J.: Entanglement of spin waves among four quantum memories. Nature 468(7322), 412–416 (2010)

    Article  ADS  Google Scholar 

  46. Hartmann, M.J., Brandão, F.G.S.L., Plenio, M.B.: Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2(12), 849–855 (2006)

    Article  Google Scholar 

  47. Hong, C., Heo, J., Kang, M.S., Jang, J., Yang, H.J., Kwon, D.: Generation of two-photon hybrid-entangled W state with photonic qubit and time-bin via cross Kerr nonlinearities. Phys. Scr. 95(8), 085104 (2020)

    Article  ADS  Google Scholar 

  48. Munhoza, P.P., Semião, F.L.: Multipartite entangled states with two bosonic modes and qubits. Eur. Phys. J. D 59(3), 509–519 (2010)

    Article  ADS  Google Scholar 

  49. Zenga, Y., Hua, M., Guo, B.: Preparation of SAM-Path-OAM hybrid entanglement W state. Optik-Int. J. Light Electron Opt. 207, 164454 (2020)

    Article  Google Scholar 

  50. Yang, C.P., Chu, S.I., Han, S.: Possible realization of entanglement, logical gates, and quantum information transfer with superconducting-quantuminterference-device qubits in cavity QED. Phys. Rev. A 67(4), 042311 (2003)

    Article  ADS  Google Scholar 

  51. You, J.Q., Nori, F.: Quantum information processing with superconducting qubits in a microwave field. Phys. Rev. B 68(6), 064509 (2003)

    Article  ADS  Google Scholar 

  52. Blais, A., Huang, R.S., Wallra, A., Girvin, S.M., Schoelkopf, R.J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69(6), 062320 (2004)

    Article  ADS  Google Scholar 

  53. You, J.Q., Nori, F.: Superconducting circuits and quantum information. Phys. Today 58(11), 42–47 (2005)

    Article  Google Scholar 

  54. Clarke, J., Wilhelm, F.K.: Superconducting quantum bits. Nature 453(7198), 1031–1042 (2008)

    Article  ADS  Google Scholar 

  55. You, J.Q., Nori, F.: Atomic physics and quantum optics using superconducting circuits. Nature 474(7353), 589–597 (2011)

    Article  ADS  Google Scholar 

  56. Xiang, Z.L., Ashhab, S., You, J.Q., Nori, F.: Hybrid quantum circuits: superconducting circuits interacting with other quantum systems. Rev. Mod. Phys. 85(2), 623–653 (2013)

    Article  ADS  Google Scholar 

  57. Li, P.B., Liu, Y.C., Gao, S.Y., Xiang, Z.L., Rabl, P., Xiao, Y.F., Li, F.L.: Hybrid quantum device based on NV centers in diamond nanomechanical resonators plus superconducting waveguide cavities. Phys. Rev. Appl. 4(4), 044003 (2015)

    Article  ADS  Google Scholar 

  58. Gu, X., Kockum, A.F., Miranowicz, A., Liu, Y.X., Nori, F.: Microwave photonics with superconducting quantum circuits. Phys. Rep. 718–719, 1–102 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  59. Woods, W., Calusine, G., Melville, A., Sevi, A., Golden, E., Kim, D.K., Rosenberg, D., Yoder, J.L., Oliver, W.D.: Determining interface dielectric losses in superconducting coplanar waveguide resonators. Phys. Rev. Appl. 12(1), 014012 (2019)

    Article  ADS  Google Scholar 

  60. Melville, A., Calusine, G., Woods, W., Serniak, K., Golden, E., Niedzielski, B.M., Kim, D.K., Sevi, A., Yoder, J.L., Dauler, E.A., Oliver, W.D.: Comparison of dielectric loss in titanium nitride and aluminum superconducting resonators. Appl. Phys. Lett. 117, 124004 (2020)

    Article  ADS  Google Scholar 

  61. Wang, C., Gao, Y.Y., Reinhold, P., Heeres, R.W., Ofek, N., Chou, K., Axline, C., Reagor, M., Blumoff, J., Sliwa, K.M., Frunzios, L., Girvin, S.M., Jiang, L., Mirrahimi, M., Devoret, M.H., Schoelkopf, R.J.: A Schrödinger cat living in two boxes. Science 352(6289), 1087–1091 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  62. Reagor, M., Pfaff, W., Axline, C., Heeres, R.W., Ofek, N., Sliwa, K., Holland, E., Wang, C., Blumoff, J., Chou, K., Hatridge, M.J., Frunzio, L., Devoret, M.H., Jiang, L., Schoelkopf, R.J.: A quantum memory with near-millisecond coherence in circuit QED. Phys. Rev. B 94(1), 014506 (2016)

    Article  ADS  Google Scholar 

  63. Hofheinz, M., Wang, H., Ansmann, M., Bialczak, R.C., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Wenner, J., Martinis, J.M., Cleland, A.N.: Synthesizing arbitrary quantum states in a superconducting resonator. Nature (London) 459(7246), 546–549 (2009)

    Article  ADS  Google Scholar 

  64. Wang, H., Hofheinz, M., Wenner, J., Ansmann, M., Bialczak, R.C., Lenander, M., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Weides, M., Cleland, A.N., Martinis, J.M.: Improving the coherence time of superconducting coplanar resonators. Appl. Phys. Lett. 95, 233508 (2009)

    Article  ADS  Google Scholar 

  65. Devoret, M.H., Schoelkopf, R.J.: Superconducting circuits for quantum information: an outlook. Science 339(6124), 1169–1174 (2013)

    Article  ADS  Google Scholar 

  66. Lu, P.M., Song, J., Xia, Y.: Implementing a multi-qubit quantum phase gate encoded by photonic qubit. Chin. Phys. Lett. 27(3), 030302 (2010)

    Article  ADS  Google Scholar 

  67. Yang, C.P., Su, Q.P., Han, S.: Generation of Greenberger–Horne–Zeilinger entangled states of photons in multiple cavities via a superconducting qutrit or an atom through resonant interaction. Phys. Rev. A 86(2), 022329 (2012)

    Article  ADS  Google Scholar 

  68. Hua, M., Tao, M.J., Deng, F.G.: Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics. Phys. Rev. A 90(1), 012328 (2014)

    Article  ADS  Google Scholar 

  69. Hua, M., Tao, M.J., Deng, F.G.: Fast universal quan tum gates on microwave photons with all-resonance operations in circuit QED. Sci. Rep. 5(1), 9274 (2015)

    Article  Google Scholar 

  70. Ye, B., Zheng, Z.F., Zhang, Y., Yang, C.P.: Circuit QED: single-step realization of a multiqubit controlled phase gate with one microwave photonic qubit simultaneously controlling \(n-1\) microwave photonic qubits. Opt. Express 26(23), 30689–30702 (2018)

    Article  ADS  Google Scholar 

  71. Han, J.X., Wu, J.L., Wang, Y., Jiang, Y.Y., Xian, Y., Song, J.: Multi-qubit phase gate on multiple resonators mediated by a superconducting bus. Opt. Express 28(2), 1954–1969 (2020)

    Article  ADS  Google Scholar 

  72. Jeong, H., Kim, M.S.: Efficient quantum computation using coherent states. Phys. Rev. A 65(4), 042305 (2002)

    Article  ADS  Google Scholar 

  73. Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88(5), 057902 (2002)

    Article  ADS  Google Scholar 

  74. Ralph, T.C., Gilchrist, A., Milburn, G.J., Munro, W.J., Glancy, S.: Quantum computation with optical coherent states. Phys. Rev. A 68(4), 042319 (2003)

    Article  ADS  Google Scholar 

  75. An, N.B.: Teleportation of coherent-state superpositions within a network. Phys. Rev. A 68(2), 022321 (2003)

    Article  ADS  Google Scholar 

  76. Guo, G.C., Zheng, S.B.: Preparation of entangled coherent states of the electromagnetic field based on detecting the state of the atom in the Jaynes–Cummings model. Opt. Commun. 133(1–6), 142–146 (1997)

    Article  ADS  Google Scholar 

  77. Yang, C.P., Su, Q.P., Zheng, S.B., Han, S.: Generating entanglement between microwave photons and qubits in multiple cavities coupled by a superconducting qutrit. Phys. Rev. A 87(2), 022320 (2013)

    Article  ADS  Google Scholar 

  78. Ofek, N., Petrenko, A., Heeres, R., Reinhold, P., Leghtas, Z., Vlastakis, B., Liu, Y., Frunzio, L., Girvin, S.M., Jiang, L., Mirrahimi, M., Devoret, M.H., Schoelkopf, R.J.: Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536(7617), 441–445 (2016)

    Article  ADS  Google Scholar 

  79. Mirrahimi, M., Leghtas, Z., Albert, V.V., Touzard, S., Schoelkopf, R.J., Jiang, L., Devoret, M.H.: Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys. 16(4), 045014 (2014)

    Article  ADS  Google Scholar 

  80. Nigg, S.E.: Deterministic Hadamard gate for microwave cat-state qubits in circuit QED. Phys. Rev. A 89(2), 022340 (2014)

    Article  ADS  Google Scholar 

  81. Zhang, Y., Zhao, X., Zheng, Z.F., Yu, L., Su, Q.P., Yang, C.P.: Universal controlled-phase gate with cat-state qubits in circuit QED. Phys. Rev. A 96(5), 052317 (2017)

    Article  ADS  Google Scholar 

  82. Heeres, R.W., Reinhold, P., Ofek, N., Frunzio, L., Jiang, L., Devoret, M.H., Schoelkopf, R.J.: Implementing a universal gate set on a logical qubit encoded in an oscillator. Nat. Commun. 8(1), 94 (2017)

    Article  ADS  Google Scholar 

  83. Liu, T., Zheng, Z.F., Zhang, Y., Fang, Y.L., Yang, C.P.: Transferring entangled states of photonic cat-state qubits in circuit QED. Front. Phys. 15(2), 21603 (2020)

    Article  ADS  Google Scholar 

  84. Zheng, S.B., Guo, G.C.: Efficient scheme for two-atom entanglement and quantum information processing in cavity QED. Phys. Rev. Lett. 85(11), 2392–2395 (2000)

    Article  ADS  Google Scholar 

  85. Sorensen, A., Molmer, K.: Quantum computation with ions in thermal motion. Phys. Rev. Lett. 82(9), 1971–1974 (1999)

    Article  ADS  Google Scholar 

  86. James, D.F.V., Jerke, J.: Effective Hamiltonian theory and its applications in quantum information. Can. J. Phys. 85(6), 625–632 (2007)

    Article  ADS  Google Scholar 

  87. Gerry, C., Knight, P.: Introductory Quantum Optics. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  88. Xu, Y., Ma, Y., Cai, W., Mu, X., Dai, W., Wang, W., Hu, L., Li, X., Han, J., Wang, H., Song, Y., Yang, Z.B., Zheng, S.B., Sun, L.: Demonstration of controlled-phase gates between two error-correctable photonic qubits. Phys. Rev. Lett. 124(12), 120501 (2020)

    Article  ADS  Google Scholar 

  89. Sandberg, M., Wilson, C.M., Persson, F., Bauch, T., Johansson, G., Shumeiko, V., Duty, T., Delsing, P.: Tuning the field in a microwave resonator faster than the photon lifetime. Appl. Phys. Lett. 92(20), 203501 (2008)

    Article  ADS  Google Scholar 

  90. Wang, Z.L., Zhong, Y.P., He, L.J., Wang, H., Martinis, J.M., Cleland, A.N., Xie, Q.W.: Quantum state characterization of a fast tunable superconducting resonator. Appl. Phys. Lett. 102(16), 163503 (2013)

    Article  ADS  Google Scholar 

  91. Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Katz, N., Lucero, E., O’Connell, A., Wang, H., Cleland, A.N., Martinis, J.M.: Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state. Nat. Phys. 4(7), 523–526 (2008)

    Article  Google Scholar 

  92. Leek, P.J., Filipp, S., Maurer, P., Baur, M., Bianchetti, R., Fink, J.M., Goppl, M., Steffen, L., Wallraff, A.: Using sideband transitions for two-qubit operations in superconducting circuits. Phys. Rev. B 79(18), 180511 (2009)

    Article  ADS  Google Scholar 

  93. Niskanen, A.O., Harrabi, K., Yoshihara, F., Nakamura, Y., Lloyd, S., Tsai, J.S.: Quantum coherent tunable coupling of superconducting qubits. Science 316(5825), 723–726 (2007)

    Article  ADS  Google Scholar 

  94. Inomata, K., Yamamoto, T., Billangeon, P.M., Nakamura, Y., Tsai, J.S.: Large dispersive shift of cavity resonance induced by a superconducting flux qubit in the straddling regime. Phys. Rev. B 86(14), 140508 (2012)

    Article  ADS  Google Scholar 

  95. Peng, Z.H., Liu, Y.X., Peltonen, J.T., Yamamoto, T., Tsai, J.S., Astafiev, O.: Correlated emission lasing in harmonic oscillators coupled via a single three-level artificial atom. Phys. Rev. Lett. 115(22), 223603 (2015)

    Article  ADS  Google Scholar 

  96. Liu, Y.X., You, J.Q., Wei, L.F., Sun, C.P., Nori, F.: Optical selection rules and phase dependent adiabatic state control in a superconducting quantum circuit. Phys. Rev. Lett. 95(8), 087001 (2005)

    Article  ADS  Google Scholar 

  97. Grimm, A., Frattini, N.E., Puri, S., Mundhada, S.O., Touzard, S., Mirrahimi, M., Girvin, S.M., Shankar, S., Devoret, M.H.: Stabilization and operation of a Kerr-cat qubit. Nature (London) 584(7820), 205–209 (2020)

    Article  ADS  Google Scholar 

  98. Kirchmair, G., Vlastakis, B., Leghtas, Z., Nigg, S.E., Paik, H., Ginossar, E., Mirrahimi, M., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Observation of quantum state collapse and revival due to the singlephoton Kerr effect. Nature (London) 495(7440), 205–209 (2013)

    Article  ADS  Google Scholar 

  99. Vlastakis, B., Kirchmair, G., Leghtas, Z., Nigg, S.E., Frunzio, L., Girvin, S.M., Mirrahimi, M., Devoret, M.H., Schoelkopf, R.J.: Deterministically encoding quantum information using 100-photon Schrodinger cat states. Science 342(6158), 607–610 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  100. Sun, L., Petrenko, A., Leghtas, Z., Vlastakis, B., Kirchmair, G., Sliwa, K.M., Narla, A., Hatridge, M., Shankar, S., Blumoff, J., Frunzio, L., Mirrahimi, M., Devoret, M.H., Schoelkopf, R.J.: Tracking photon jumps with repeated quantum nondemolition parity measurements. Nature (London) 511(7510), 444–448 (2014)

    Article  ADS  Google Scholar 

  101. Vlastakis, B., Petrenko, A., Ofek, N., Sun, L., Leghtas, Z., Sliwa, K., Liu, Y., Hatridge, M., Blumoff, J., Frunzio, L., Mirrahimi, M., Jiang, L., Devoret, M.H., Schoelkopf, R.J.: Characterizing entanglement of an artificial atom and a cavity cat state with Bell’s inequality. Nat. Commun. 6(1), 8970 (2015)

    Article  ADS  Google Scholar 

  102. Yan, F., Gustavsson, S., Kamal, A., Birenbaum, J., Sears, A.P., Hover, D., Gudmundsen, T.J., Yoder, J.L., Orlando, T.P., Clarke, J., Kerman, A.J., Oliver, W.D.: The flux qubit revisited to enhance coherence and reproducibility. Nat. Commun. 7(1), 12964 (2016)

    Article  ADS  Google Scholar 

  103. You, J.Q., Hu, X., Ashhab, S., Nori, F.: Low-decoherence flux qubit. Phys. Rev. B 75(14), 140515 (2007)

    Article  ADS  Google Scholar 

  104. Niemczyk, T., Deppe, F., Huebl, H., Menzel, E.P., Hocke, F., Schwarz, M.J., Garcia Ripoll, J.J., Zueco, D., Hümmer, T., Solano, E., Marx, A., Gross, R.: Circuit quantum electrodynamics in the ultrastrong-coupling regime. Nat. Phys. 6(10), 772–776 (2010)

    Article  Google Scholar 

  105. Baur, M., Filipp, S., Bianchetti, R., Fink, J.M., Göppl, M., Steffen, L., Leek, P.J., Blais, A., Wallraff, A.: Measurement of Autler–Townes and Mollow transitions in a strongly driven superconducting qubit. Phys. Rev. Lett. 102(24), 243602 (2009)

    Article  ADS  Google Scholar 

Download references

Funding

This work was partly supported by the National Natural Science Foundation of China (NSFC) (11374083, 11774076, U21A20436), Innovation Program for Quantum Science and Technology (2021ZD0301705), and the Jiangsu Funding Program for Excellent Postdoctoral Talent.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chui-Ping Yang.

Ethics declarations

Conflict of interest

The authors declare 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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Su, QP., Bin, L., Zhang, Y. et al. Generation of a hybrid W entangled state of three photonic qubits with different encodings. Quantum Inf Process 23, 16 (2024). https://doi.org/10.1007/s11128-023-04227-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-04227-3

Keywords

Navigation