Entanglemnt in nonlinear three-qubits Jaynes — Cummings model

A. R. Bagrov ; E. K. Bashkirov

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 1, pp. 89-101

Résumé

In this paper, we investigated the dynamics of entanglement of pairs of qubits in a system of three identical qubits that interact non-resonantly with the selected mode of a microwave resonator without loss with the Kerr medium by means of single-photon transitions. We have found solutions to the quantum time Schrodinger equation for the total wave function of the system for the initial separable, biseparable and true entangled states of qubits and the Fock initial state of the resonator field. Based on these solutions, the criterion of entanglement of qubit pairs — negativity is calculated. The results of numerical simulation of the negativity of qubit pairs have shown that the presence of disorder and Kerr nonlinearity in the case of an initial non-entangled state of a pair of qubits can lead to a significant increase in the degree of their entanglement. In the case of an initial entangled state of a pair of qubits, the disorder and the Kerr medium can lead to a significant stabilization of the initial entanglement.

Détail

Keywords: qubits, not-resonant interaction, cavity, Kerr nonlinearity, negativity, sudden death of entanglement.
Mots-clés : one-photon transitions, entanglement

Bibliographie

[1] Kendon V.M., Nemoto K., Munro W.J., “Typical entanglement in multi-qubit systems”, Journal of Modern Optics, 49:10 (2002), 1709–1716 | DOI | MR | Zbl

[2] Most Y., Shimoni Y., Biham O., “Formation of multipartite entanglement using random quantum gates”, Physical Review A: Atomic, molecular, and optical physics, 76:2 (2007), 022328 | DOI | MR

[3] Zhi P., Hu Y., “Construct maximally five- and seven-qubit entangled states via three-qubit GHZ state”, International Journal of Theoretical Physics, 36:30 (2022), 2250215 | DOI | MR

[4] Kazuyuki F., Kyoko H., Ryosuke K., Tatsuo S., Yukako W., “Explicit Form of the Evolution Operator of TAVIS-CUMMINGS Model: Three and Four Atoms Cases”, International Journal of Geometric Methods in Modern Physics, 1:6 (2012), 721–730 | DOI

[5] Rinner S.J., Pittorino T., “Generation of Multipartite Entangled States Using Switchable Coupling of Cooper-Pair-Boxes”, Journal of Modern Physics, 11:10 (2020), 1514–1527 | DOI

[6] Wendin G., “Quantum information processing with super-conducting circuits: a review”, Reports on Progress in Physics, 80:10 (2017), 106001 | DOI | MR

[7] Kjaergaard M., Schwartz M.E., Braumüller J., Krantz P., Wang J.-I., Gustavsson S., Oliver W.D., “Superconducting Qubits: Current State of Play”, Annual Reviews of Condensed Matter Physics, 11 (2020), 369–395 | DOI

[8] Huang H.-L., Wu D., Fan D., Zhu X., “Superconducting quantum computing: a review”, Science China. Information Sciences, 63 (2020), 180501 | DOI | MR

[9] Chen J., “Review on Quantum Communication and Quantum Computation”, Journal of Physics: Conference Series, 1865 (2021), 022008 | DOI

[10] Biamonte J., Faccin M., De Domenico M., “Complex Networks: from Classical to Quantum”, Communications Physics, 2 (2019), 53 | DOI

[11] Mooney G.J., Hill C.D., Hollenberg L.C.L., “Entanglement in a 20-Qubit Superconducting Quantum Computer”, Scientific Reports, 9 (2019), 13465 | DOI

[12] Apollaro T. J. G., Lorenzo S., Plastina F., Consiglio M., Zyczkowski K., “Entangled States Are Harder to Transfer than Product States”, Entropy, 25:1 (2023), 46 | DOI | MR

[13] Nieman K., Rangan K.K., Durand H., “Control Implemented on Quantum Computers: Effects of Noise, Nondeterminism, and Entanglement”, Industrial and Engineering Chemistry Research, 61:28 (2022), 10133–10155 | DOI

[14] Arute F. et al., “Quantum supremacy using a programmable superconducting processor”, Nature, 574 (2019), 505–510 | DOI

[15] Ball P., “First quantum computer to pack 100 qubits enters crowded race”, Nature, 599:7886 (2021), 542 | DOI

[16] Lacroix D., “Symmetry-Assisted Preparation of Entangled Many-Body States on a Quantum Computer”, Physical Review Letters, 125 (2020), 230502 | DOI | MR

[17] Peres A., “Separability Criterion for Density Matrices”, Physical Review Letters, 77 (1996), 1413–1415 | DOI | MR | Zbl

[18] Horodecki R., Horodecki M., Horodecki P., “Separability of Mixed States: Necessary and Sufficient Condition”, Physics Letters A, 223 (1996), 333–339 | DOI | MR

[19] Wootters W.K., “Entanglement of Formation of an Arbitrary State of Two Qubits”, Physical Review Letters, 80:10 (1998), 2245 | DOI | Zbl

[20] Zha X., Yuan C., Zhang Y., “Generalized criterion for a maximally multi-qubit entangled state”, Laser Physics Letters, 10:4 (1998), 045201 | DOI

[21] Filippov S.N., “Quantum Mappings and Characterization of Entangled Quantum States”, Journal of Mathematical Sciences, 241 (2019), 210–236 | DOI | MR | Zbl

[22] Seevinck M., Gühne O., “Separability criteria for genuine multiparticle entanglement”, New Journal of Physics, 12 (2010), 053002 | DOI | Zbl

[23] Pereira L., Zambrano L., Delgado A., “Scalable estimation of pure multi-qubit states”, npj Quantum Information, 8 (2022), 57 | DOI

[24] Zhahir A. A., Mohd S. M., Shuhud M.I.M., Idrus B., Zainuddin H., Jan N.M., Wahiddin M., “Entanglement Quantification and Classification: A Systematic Literature Review”, International Journal of Advanced Computer Science and Applications, 13:5 (2022), 218–225 | DOI

[25] Dur W., Cirac J.I., “Classification of multiqubit mixed states: Separability and distillability properties”, Physical Review A: Atomic, molecular and optical physics, 61 (2000), 042314 | DOI | MR

[26] Dur W., Cirac J.I., Vidal G., “Three qubits can be entangled in two inequivalent ways”, Physical Review A: Atomic, molecular, and optical physics, 62 (2000), 062314 | DOI | MR

[27] Acin A., Bruß D., Lewenstein M., Sanpera A., “Classification of Mixed Three-Qubit States”, Physical Review Letters, 87 (2000), 040401 | DOI | MR

[28] Garcia-Alcaine G., Sabin C., “A classification of entanglement in three-qubit systems”, The European Physical Journal D, 48 (2008), 435–442 | DOI | MR

[29] Siti Munirah Mohd S.M., Idrus B., Zainuddin H., Mukhtar M., “Entanglement Classification for a Three-qubit System using Special Unitary Groups”, International Journal of Advanced Computer Science and Applications, 10:7 (2019), 374–379 | DOI

[30] Akbari-Kourbolagh Y., “Entanglement criteria for the three-qubit states”, International Journal of Quantum Information, 15:7 (2017), 1750049 | DOI | MR | Zbl

[31] Bagrov A.R., Bashkirov E.K., “Dynamics of the three-qubits Tavis - Cummings model”, Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 28:1–2 (2022), 95–105 (In Russ.) | DOI | MR

[32] Zhang B., “Entanglement between two qubits interacting with a slightly detuned thermal field”, Optics Communications, 283:23 (2010), 4676–4679 | DOI

[33] Bashkirov E.K., “Thermal Entanglement Between a Jaynes — Cummings Atom and an Isolated Atom”, International Jornal of Theoretical Physics, 57:12 (2018), 3761–3771 | DOI | Zbl

[34] Al Naim A.F., Khan J.Y., Khalil E.M., Abdel-Khalek S., “Effects of Kerr Medium and Stark Shift Parameter on Wehrl Entropy and the Field Purity for Two-Photon Jaynes-Cummings Model Under Dispersive Approximation”, Journal of Russian Laser Research, 40:1 (2019), 20–29 | DOI

[35] Aldaghfag S.A., Berrada K., Abdel-Khalek S., “Entanglement and photon statistics of two dipole-dipole coupled superconducting qubits with Kerr-like nonlinearities”, Results in Physics, 16 (2020), 102978 | DOI

[36] Bashkirov E.K., “Thermal entanglement in Tavis-Cummings models with Kerr media”, Proceedings of SPIE, 12193, 2022, 121930Q | DOI | MR