(49-6) 05 * << * >> * Russian * English * Content * All Issues

Analysis of the behavior of entanglement parameters for the three-qubit Tavis-Cummings model with multiphoton processes
A.R. Bagrov 1, E.K. Bashkirov 1

1 Samara National Research University,
Moskovskoye Shosse 34, Samara, 443086, Russia

 PDF, 1201 kB

DOI: 10.18287/2412-6179-CO-1679

Pages: 899-908.

Full text of article: Russian language.

Abstract:
In this paper, we analyze in detail the dynamics of the negativity criterion, fidelity and concurrence fill for the Tavis-Cummings model in which three qubits are in a common single-mode ideal resonator and interact resonantly with the field mode via multiphoton processes. By solving the unsteady Schrödinger equation, we give analytic solutions for genuine entangled Werner- and Greenberger-Horn-Zeilinger states. It is shown that the multiplicity of photon transitions can significantly stabilize the genuine entangled states of both types. Key features in the dynamics pattern of the entanglement parameters are highlighted. We conclude that the negativity criterion is not suitable for describing the dynamics of entanglement of qubits in the case of three-qubit Greenberger-Horn-Zeilinger states. Main advantages of the concurrence fill over the negativity criterion are shown.

Keywords:
qubits, multiphoton processes, negativity, fidelity, concurrence fill, resonator.

Citation:
Bagrov AR, Bashkirov EK. Analysis of the behavior of entanglement parameters for the three-qubit Tavis-Cummings model with multiphoton processes. Computer Optics 2025; 49(6): 899-908. DOI: 10.18287/2412-6179-CO-1679.

Acknowledgements:
The work was partly funded by the Ministry of Science and Higher Education of the Russian Federation under the government project N FSSS-2025-0003.

References:
  1. Chia C, Huang D, Leong V, Kong JF, Goh KEJ. Hybrid quantum systems with artificial atoms in solid state. Adv Quantum Technol 2024; 7: 2300461. DOI: 10.1002/qute.202300461.
  2. Nielsen MA, Chuang IL. Quantum computation and quantum information. 10th ed. Cambridge: Cambridge University Press; 2010. ISBN: 9781107002173.
  3. Barshak EV, Lapin BP, Vikulin DV, Alieva SS, Alexeyev CN, Yavorsky MA. All-fiber SWAP-CNOT gate for optical vortices. Computer Optics 2021; 45(6): 853-859. DOI: 10.18287/2412-6179-CO-938.
  4. Barnes E, Arenz C, Pitchford AJG, Economou SE. Fast microwave-driven three-qubit gates for cavity-coupled superconducting qubits. Phys Rev B 2017; 96(2): 024504. DOI: 10.1103/PhysRevB.96.024504.
  5. Reed MD, DiCarlo L, Nigg SE, Sun L, Frunzio L, Girvin SM, Schoelkopf RJ. Realization of three-qubit quantum error correction with superconducting circuits. Nature 2012; 482: 382-385. DOI: 10.1038/nature10786.
  6. Moskalenko IN, Simakov IA, Abramov NN, et al. High fidelity two-qubit gates on fluxoniums using a tunable coupler. npj Quantum Inf 2022; 8: 130. DOI: 10.1038/s41534-022-00644-x.
  7. Wei H, Tang J, Deng Y. N-photon bundles emission in high-spin Jaynes–Cummings model. New J Phys 2024; 26(12): 123024. DOI: 10.1088/1367-2630/ad9d6e.
  8. Perminov NS, Petrovnin KV, Gerasimov KI, Kirillov RS, Latypov RR, Sherstyukov ON, Moiseev SA. Spectroscopy of cascade multiresonator quantum memory. Computer Optics 2018; 42(4): 614-619. DOI: 10.18287/2412-6179-2018-42-4-614-619.
  9. Muñoz CS, del Valle Tudela EAG, Müller K, Lichtmannecker S, Kaniber M, Tejedor C, Finley J, Laussy F. Emitters of N-photon bundles. Nat Photon 2014; 8(7): 550-555. DOI: 10.1038/nphoton.2014.114.
  10. Bashkirov EK, Mastyugin MS. Entanglement of two superconducting qubits interacting with two-mode thermal field. Computer Optics 2013; 37(3): 278-285. DOI: 10.18287/0134-2452-2013-37-3-278-285.
  11. Bashkirov EK. Dynamics of entanglement of atoms with two-photon transitions induced by a thermal field. Computer Optics 2020; 44(2): 167-176. DOI: 10.18287/2412-6179-CO-595.
  12. Campagne-Ibarcq P, Zalys-Geller E, Narla A, Shankar S, Reinhold P, Burkhart L, Axline C, Pfaff W, Frunzio L, Schoelkopf RJ, Devoret MH. Deterministic remote entanglement of superconducting circuits through microwave two-photon transitions. Phys Rev Lett 2018; 120: 200501. DOI: 10.1103/PhysRevLett.120.200501.
  13. Smith WC, Borgognoni A, Villiers M, Roverc’h E, Palomo J, Delbecq MR, Kontos P. Campagne-Ibarcq TP, Doucot B, Leghtas Z. Spectral signature of high-order photon processes mediated by Cooper-pair pairing. arXiv Preprint. 2023. Source: <https://arxiv.org/abs/2312.15075>. DOI: 10.48550/arXiv.2312.15075.
  14. Adhikari P, Hafezi M, Taylor JM. Nonlinear optics quantum computing with circuit QED. Phys Rev Lett 2013; 110(6): 060503. 10.1103/PhysRevLett.110.060503.
  15. Villas-Boas1 CJ, Rossatto DZ. Multiphoton Jaynes-Cummings model: Arbitrary rotations in fock space and quantum filters. Phys Rev Lett 2019; 122: 123604. DOI: 10.1103/PhysRevLett.122.123604.
  16. Bagrov AR, Bashkirov EK. Thermal entanglement in the three-qubit Tavis-Cummings model with Kerr nonlinearity. Computer Optics 2025; 49(1): 53-59. DOI: 10.18287/2412-6179-CO-1544.
  17. Dür W, Vidal G, Cirac JI. Three qubits can be entangled in two inequivalent ways. Phys Rev A 2000; 62(6): 062314. DOI: 10.1103/PhysRevA.62.062314.
  18. Biryukov AA, Shleenkov MA. Mathematical modeling of processes in quantum computer elements based on methods of quantum theory to improve their efficiency. Computer Optics 2024; 48(6): 889-893. DOI: 10.18287/2412-6179-CO-1489.
  19. Jozsa R. Fidelity for mixed quantum states. J Mod Opt 1994; 41(12): 2315-2323. DOI: 10.1080/09500349414552171.
  20. Xie S, Eberly JH. Triangle measure of tripartite entanglement. Phys Rev Lett 2021; 127: 040403. DOI: 10.1103/PhysRevLett.127.040403.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20