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Evolution of the entanglement, photon statistics and quantum Fisher information of a single qubit parity deformed JCM

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Abstract

In this paper we use the atomic version of the quantum Fisher information to estimate the quantum state of the parity deformed Jaynes Cummings Model (PD-JCM) that describing the interaction between a SQ (single qubit) and parity deformed field. The nonclassical properties of the field are identified by the evolution of the second-order correlation function. The von Neumann entropy is provided for the non-local correlation between the SQ and parity deformed field. Also, the single qubit quantum Fisher information within the phase shift estimator is obtained and compared with the von Neumann entropy during the interaction time. We examine the effect of the deformation parameter and time-dependent coupling or qubit speed on the dynamical behavior of the proposed quantities. The results verified that the dynamical behavior of the proposed quantities can be controlled by the qubit speed, deformation parameter and time-dependent coupling or qubit speed parameters.

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References

  • Abdalla, M.S., Khalil, E.M., Obada, A.S.F., Peřina, J., Křepelka, J.: Linear entropy and squeezing of the interaction between two quantum system described by su (1, 1) and su(2) Lie group in presence of two external terms. AIP Adv. 7, 015013 (2017)

    ADS  Google Scholar 

  • Abdel-Khalek, S.: Quantum Fisher information for moving three-level atom. Quantum Inf. Process. 12(12), 3761–3769 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  • Abdel-Khalek, S.: Quantum entanglement and geometric phase of two moving two-level atoms. Open Syst. Inf. Dyn. 22(3), 1550015 (2015)

    MathSciNet  MATH  Google Scholar 

  • Abdel-Khalek, S., Berrada, K., Obada, A.S.F.: Quantum Fisher information for a single qubit system. Eur. Phys. J. D 66(3), 1–6 (2012)

    MATH  Google Scholar 

  • Abdel-Khalek, S., A Halawani, S.H., Obada, A.S.: Effect of time dependent coupling on the dynamical properties of the nonlocal correlation between two three-level atoms. Int. J. Theor. Phys. 56(9), 2898–2910 (2017)

    MathSciNet  MATH  Google Scholar 

  • Abd-Rabbou, M.Y., Metwally, N., Ahmed, M.M.A., Obada, A.S.: Suppressing the information losses of accelerated qubit–qutrit system. Int. J. Quantum Inf. 17(4), 1950032 (2019a)

    MathSciNet  MATH  Google Scholar 

  • Abd-Rabbou, M.Y., Metwally, N., Obada, A.F., Ahmed, M.M.A.: Restraining the decoherence of accelerated qubit–qutrit system via local Markovian channels. Phys. Scr. 94(10), 105103 (2019b)

    ADS  Google Scholar 

  • Åberg, J.: Catalytic coherence. Phys. Rev. Lett. 113(15), 150402 (2014)

    ADS  Google Scholar 

  • Abo-Kahla, D.A.M., Abd-Rabbou, M.Y., Metwally, N.: The orthogonality speed of two-qubit state interacts locally with spin chain in the presence of Dzyaloshinsky-Moriya interaction. Laser Phys. Lett. 18(4), 045203 (2021)

    ADS  Google Scholar 

  • Agarwal, G.S., Tara, K.: Nonclassical properties of states generated by the excitations on a coherent state. Phys. Rev. A 43, 492 (1991)

    ADS  Google Scholar 

  • Al Naim, A.F., Khan, J.Y., Abdel-Khalek, S., Khalil, E.M.: Entanglement and physical attributes of the interaction between two SC-qubits and thermal field in the presence of a magnetic field. Microelectron. J. 86, 15–21 (2019)

    Google Scholar 

  • Almarashi, A.M., Algarni, A., Abdel-Khalek, S., Ng, H.K.T.: Quantum Fisher information and tomographic entropy of a single qubit in excited binomial and negative binomial distributions. J. Russ. Laser Res. 40(4), 313–320 (2019)

    Google Scholar 

  • Barndorff-Nielsen, O.E., Gill, R.D., Jupp, P.E.: On quantum statistical inference. J. r. Stat. Soc. B 65, 775 (2003)

    MathSciNet  MATH  Google Scholar 

  • Berrada, K., Fanchini, F.F., Abdel-Khalek, S.: Quantum correlations between each qubit in a two-atom system and the environment in terms of interatomic distance. Phys. Rev. A 85(5), 052315 (2012)

    ADS  Google Scholar 

  • Bose, S., Jacobs, K., Knight, P.L.: Preparation of nonclassical states in cavities with a moving mirror. Phys. Rev. A 56(5), 4175 (1997)

    ADS  Google Scholar 

  • Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72(22), 3439 (1994)

    ADS  MathSciNet  MATH  Google Scholar 

  • Dakna, M., Knöll, L., Welsch, D.G.: Photon-added state preparation via conditional measurement on a beam splitter. Opt. Commun. 145(1–6), 309–321 (1998)

    ADS  Google Scholar 

  • Dattoli, G., Gallardo, J., Torre, A.: Binomial states of the quantized radiation field. J. Opt. Soc. Am. B 2, 185–187 (1987)

    ADS  Google Scholar 

  • Dehghani, A., Mojaveri, B., Shirin, S., Faseghandis, S.A.: Parity deformed Jaynes-Cummings model: “Robust Maximally Entangled States.” Sci. Rep. 6(1), 1–15 (2016)

    Google Scholar 

  • Demkowicz-Dobrzański, R., Maccone, L.: Using entanglement against noise in quantum metrology. Phys. Rev. Lett. 113(25), 250801 (2014)

    ADS  Google Scholar 

  • Dodonov, V.V., Korennoy, Y.A., Man’ko, V.I., Moukhin, Y.A.: Non-classical properties of states generated by the excitations of even/odd coherent states of light. Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 8(3), 413 (1996)

    ADS  Google Scholar 

  • Domínguez, M.S., Vinck-Posada, H., Gómez, E.A.: Entanglement generation between two solid-state qubits mediated by microwave photons. Phys. Lett. A 388, 127045 (2021)

    MathSciNet  Google Scholar 

  • Fan, H.Y., Jing, S.C.: Connection of a type of q-deformed binomial state with q-spin coherent states. Phys. Rev. A 50, 1909 (1994)

    Google Scholar 

  • Feller, W.: Introduction to Probability, Theory and Its Applications, vol. 1, 2nd edn. Wiley (1957)

    MATH  Google Scholar 

  • Fu, S., Luo, S., Zhang, Y.: Converting nonclassicality to quantum correlations via beamsplitters. EPL (europhys. Lett.) 128(3), 30003 (2020)

    ADS  Google Scholar 

  • Giovannetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science 306(5700), 1330–1336 (2004)

    ADS  Google Scholar 

  • Glauber, R.J.: Coherent and incoherent states of the radiation field. Phys. Rev. 131(6), 2766 (1963)

    ADS  MathSciNet  MATH  Google Scholar 

  • Hoffman, A.J., Srinivasan, S.J., Schmidt, S., Spietz, L., Aumentado, J., Türeci, H.E., Houck, A.A.: Dispersive photon blockade in a superconducting circuit. Phys. Rev. Lett. 107(5), 053602 (2011)

    ADS  Google Scholar 

  • Jing, S.C., Fan, H.Y.: q-Deformed binomial state. Phys. Rev. A 49(4), 2277–2279 (1994)

    MathSciNet  Google Scholar 

  • Jones, G.N., Haight, J., Lee, C.T.: Nonclassical effects in the photon-added thermal state. Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 9(3), 411 (1997)

    ADS  Google Scholar 

  • Joshi, A., Puri, R.R.: Effects of atomic coherence on collapses and revivals in the binomial state of the field. J. Mod. Opt. 36, 557–570 (1989)

    ADS  Google Scholar 

  • Leggett, A.J.: Macroscopic quantum systems and the quantum theory of measurement. Prog. Theor. Phys. Suppl. 69, 80–100 (1980)

    ADS  MathSciNet  Google Scholar 

  • Liu, Y.X., Xu, X.W., Miranowicz, A., Nori, F.: From blockade to transparency: controllable photon transmission through a circuit-QED system. Phys. Rev. A 89(4), 043818 (2014)

    ADS  Google Scholar 

  • Lostaglio, M., Jennings, D., Rudolph, T.: Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat. Commun. 6(1), 1–9 (2015)

    Google Scholar 

  • Man’ko, V.I., Wünsche, A.: Properties of squeezed-state excitations. Quantum Semiclassical Opt. J. Eur. Opt. Soc. Part B 9(3), 381 (1997)

    ADS  Google Scholar 

  • Miranowicz, A., Bartkowiak, M., Wang, X., Liu, Y.X., Nori, F.: Testing nonclassicality in multimode fields: a unified derivation of classical inequalities. Phys. Rev. A 82(1), 013824 (2010)

    ADS  Google Scholar 

  • Mojaveri, B., Dehghani, A.: Even and odd Wigner negative binomial states: nonclassical properties. Mod. Phys. Lett. A 30(37), 1550198 (2015a)

    ADS  MathSciNet  MATH  Google Scholar 

  • Mojaveri, B., Dehghani, A.: Even and odd Wigner negative binomial states: nonclassical properties. Mod. Phys. Lett. A 30, 1550198 (2015b)

    ADS  MathSciNet  MATH  Google Scholar 

  • Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge. ISBN: 9781139495486 (2000)

  • Perelemov, A.M.: Generalized coherent states and some of their applications. Sov. Phys. Usp. 20, 703 (1977)

    ADS  Google Scholar 

  • Phoenix, S.J.D., Knight, P.L.: Fluctuations and entropy in models of quantum optical resonance. Ann. Phys. 186(2), 381–407 (1988)

    ADS  MATH  Google Scholar 

  • Scully, M.O., Zubairy, M.S.: Quantum Optics, pp. 111ff. Cambridge University Press. ISBN: 978-1-139-64306-1 (1997)

  • Shahandeh, F., Lund, A.P., Ralph, T.C.: Quantum correlations and global coherence in distributed quantum computing. Phys. Rev. A 99, 052303 (2019)

    ADS  Google Scholar 

  • Stoler, D., Saleh, B.E.A., Teich, M.C.: Binomial states of the quantized radiation field. Opt. Acta 32, 345 (1985)

    ADS  MathSciNet  Google Scholar 

  • Vedral, V.: Quantifying entanglement in macroscopic systems. Nature 453, 1004–1007 (2008)

    ADS  Google Scholar 

  • Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78(12), 2275 (1997)

    ADS  MathSciNet  MATH  Google Scholar 

  • Vidiella-Barranco, A., Roversi, J.A.: Quantum superpositions of binomial states of light. J. Mod. Opt. 42, 2475–2493 (1995)

    ADS  Google Scholar 

  • Xinyue, L., et al.: Entanglement-enhanced quantum metrology in colored noise by quantum zeno effect. Phys. Rev. Lett. 129(7), 070502 (2022)

    Google Scholar 

  • Yu, M., Liu, Y., Yang, P., Gong, M., Cao, Q., Zhang, S., Cai, J.: Quantum Fisher information measurement and verification of the quantum Cramér-Rao bound in a solid-state qubit. Npj Quantum Inf. 8(1), 1–8 (2022)

    Google Scholar 

  • Zhang, L., Jia, F., Zhang, H., Ye, W., Xia, Y., Hu, L., Huang, J.: Improving entanglement of even entangled coherent states via superposition of number-conserving operations. Results Phys. 35, 105324 (2022)

    Google Scholar 

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Acknowledgement

The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4300218DSR01) and Taif University Researchers Supporting Project under number TURSP-2020/154, Taif University, Taif, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, College of Science, Taif University, PO Box 11099, Taif, 21944, Saudi Arabia

    S. Abdel-Khalek & E. M. Khalil

  2. Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Adel Bandar Alruqi

  3. Department of Physics, Faculty of Applied Science, Umm Al-Qura University, PO Box 6055, Makkah, 21955, Saudi Arabia

    Marwan Ahmed Althomali

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  1. S. Abdel-Khalek
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  2. E. M. Khalil
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  3. Adel Bandar Alruqi
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Correspondence to S. Abdel-Khalek.

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Abdel-Khalek, S., Khalil, E.M., Alruqi, A.B. et al. Evolution of the entanglement, photon statistics and quantum Fisher information of a single qubit parity deformed JCM. Opt Quant Electron 55, 161 (2023). https://doi.org/10.1007/s11082-022-04365-5

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