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Intrinsic decoherence effects on correlated coherence and quantum discord in XXZ Heisenberg model

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Abstract

Spin qubits are at the heart of technological advances in quantum processors and offer an excellent framework for quantum information processing. This work characterizes the time evolution of coherence and nonclassical correlations in a two-spin XXZ Heisenberg model, from which a two-qubit system is realized. We study the effects of intrinsic decoherence on coherence (correlated coherence) and nonclassical correlations (quantum discord), taking into consideration the combined impact of an external magnetic field, Dzyaloshinsky–Moriya (DM) and Kaplan–Shekhtman–Entin–Wohlman–Aharony (KSEA) interactions. To fully understand the effects of intrinsic decoherence, two extended Werner-like (EWL) states were considered in this work. The findings indicate that intrinsic decoherence leads to a decay in the quantum coherence and quantum correlations and that their behavior depends strongly on the initial EWL state parameters. Likewise, we found that the robustness of correlated coherence and quantum discord can be controlled through an appropriate choice of the initial state. These findings give us insights into engineering a quantum system to achieve quantum advantages.

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This work is theoretical and all data is in the manuscript.

References

  • Adesso, G., Bromley, T.R., Cianciaruso, M.: Measures and applications of quantum correlations. J. Phys. A: Math. Theor. 49(47), 473001 (2016)

    MathSciNet  MATH  ADS  Google Scholar 

  • Ali, M., Rau, A., Alber, G.: Erratum: Quantum discord for two-qubit X states [Phys. Rev. A 81, 042105 (2010)],. Phys. Rev. A 82(6), 069902 (2010)

    ADS  Google Scholar 

  • El Anouz, K., Onyenegecha, C., Opara, A., Salah, A., El Allati, A.: Dynamics of quantum Fisher information and quantum coherence of two interacting atoms under time-fractional analysis. JOSA B 39(4), 979–989 (2022)

    ADS  Google Scholar 

  • Baba, H., Kaydi, W., Daoud, M., Mansour, M.: Entanglement of formation and quantum discord in multipartite j-spin coherent states. Int. J. Mod. Phys. B 34(26), 2050237 (2020)

    MathSciNet  MATH  ADS  Google Scholar 

  • Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113(14), 140401 (2014)

    ADS  Google Scholar 

  • Chaouki, E., Dahbi, Z., Mansour, M.: Dynamics of quantum correlations in a quantum dot system with intrinsic decoherence effects. Int. J. Mod. Phys. B 36(22), 2250141 (2022)

    ADS  Google Scholar 

  • Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit \(X\) states. Phys. Rev. A 84, 042313 (2011)

    ADS  Google Scholar 

  • Citro, R., Orignac, E.: Effects of anisotropic spin-exchange interactions in spin ladders. Phys. Rev. B 65(13), 134413 (2002)

    ADS  Google Scholar 

  • Coopmans, L., Kiely, A., De Chiara, G., Campbell, S.: Optimal control in disordered quantum systems. arXiv preprint arXiv:2201.02029 (2022)

  • Cruz, C., Anka, M.F., Reis, M.S., Bachelard, R., Santos, A.C.: Quantum battery based on quantum discord at room temperature. Quantum Sci. Technol. 7(2), 025020 (2022)

    ADS  Google Scholar 

  • Dahbi, Z., Mansour, M., El Allati, A.: Dynamics of quantum correlations in two 2-level atoms coupled to thermal reservoirs. Phys. Scr. 98(1), 015102 (2023)

    ADS  Google Scholar 

  • Dahbi, Z., Rahman, A.U., Mansour, M.: Skew information correlations and local quantum fisher information in two gravitational cat states. Phys. A: Stat. Mech. Appl. 609, 128333 (2022)

    MathSciNet  MATH  Google Scholar 

  • Dahbi, Z., Anka, M.F., Mansour, M., Rojas, M., Cruz, C.: Effect of induced transition on the quantum entanglement and coherence in two-coupled double quantum dots system. arXiv e-prints, pp. arXiv–2211 (2022)

  • Doggen, E.V., Schindler, F., Tikhonov, K.S., Mirlin, A.D., Neupert, T., Polyakov, D.G., Gornyi, I.V.: Many-body localization and delocalization in large quantum chains. Phys. Rev. B 98(17), 174202 (2018)

    ADS  Google Scholar 

  • Dowling, J.P., Milburn, G.J.: “Quantum technology: the second quantum revolution,’’ Philosophical transactions of the royal society of London. Seri. A Math. Phys. Eng. Sci. 361(1809), 1655–1674 (2003)

    Google Scholar 

  • Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935)

    MATH  ADS  Google Scholar 

  • Ekert, A.K., Rarity, J.G., Tapster, P.R., Palma, G.M.: Practical quantum cryptography based on two-photon interferometry. Phys. Rev. Lett. 69(9), 1293 (1992)

    ADS  Google Scholar 

  • Elghaayda, S., Dahbi, Z., Mansour, M.: Local quantum uncertainty and local quantum Fisher information in two-coupled double quantum dots. Opt. Quant. Electron. 54(7), 1–15 (2022)

    Google Scholar 

  • Elghaayda, S., Dahbi, Z., Mohamed, A.B., Mansour, M.: Nonlocal quantum correlations in a bipartite quantum system coupled to a bosonic non-Markovian reservoir. Modern Phys. Lett. A 37, 2250175 (2022)

    MathSciNet  ADS  Google Scholar 

  • Essakhi, M., Khedif, Y., Mansour, M., Daoud, M.: Intrinsic decoherence effects on quantum correlations dynamics. Opt. Quant. Electron. 54(2), 1–15 (2022)

    Google Scholar 

  • Fanchini, F., Werlang, T., Brasil, C., Arruda, L., Caldeira, A.: Non-Markovian dynamics of quantum discord. Phys. Rev. A 81(5), 052107 (2010)

    ADS  Google Scholar 

  • Ferreira, M., Rojas, O., Rojas, M.: Thermal entanglement and quantum coherence of a single electron in a double quantum dot with Rashba Interaction. arXiv preprint arXiv:2203.06301 (2022)

  • Filgueiras, C., Rojas, O., Rojas, M.: Thermal entanglement and correlated coherence in two coupled double quantum dots systems. Ann. Phys. 532(8), 2000207 (2020)

    MathSciNet  Google Scholar 

  • Haddadi, S., Hu, M.-L., Khedif, Y., Dolatkhah, H., Pourkarimi, M.R., Daoud, M.: Measurement uncertainty and dense coding in a two-qubit system: Combined effects of bosonic reservoir and dipole-dipole interaction. Results Phys. 32, 105041 (2022)

    Google Scholar 

  • Haddadi, S., Pourkarimi, M.R., Akhound, A., Ghominejad, M.: Thermal quantum correlations in a two-dimensional spin star model. Mod. Phys. Lett. A 34(22), 1950175 (2019)

    MathSciNet  MATH  ADS  Google Scholar 

  • Hashem, M., Mohamed, A.-B.A., Haddadi, S., Khedif, Y., Pourkarimi, M.R., Daoud, M.: Bell nonlocality, entanglement, and entropic uncertainty in a Heisenberg model under intrinsic decoherence: DM and KSEA interplay effects. Appl. Phys. B 128(4), 1–10 (2022)

    Google Scholar 

  • Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A: Math. Gen. 34, 6899 (2001)

    MathSciNet  MATH  ADS  Google Scholar 

  • Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A: Math. Gen. 34(35), 6899 (2001)

    MathSciNet  MATH  ADS  Google Scholar 

  • Huang, Y.: Quantum discord for two-qubit X states: analytical formula with very small worst-case error. Phys. Rev. A 88(1), 014302 (2013)

    ADS  Google Scholar 

  • Huang, Y.: Computing quantum discord is NP-complete. New J. Phys. 16(3), 033027 (2014)

    MathSciNet  MATH  ADS  Google Scholar 

  • Kaplan, T.: Single-band hubbard model with spin-orbit coupling. Zeitschrift für Physik B Condensed Matter 49(4), 313–317 (1983)

    ADS  Google Scholar 

  • Khedif, Y., Haddadi, S., Pourkarimi, M.R., Daoud, M.: Thermal correlations and entropic uncertainty in a two-spin system under DM and KSEA interactions. Mod. Phys. Lett. A 36(29), 2150209 (2021)

    MathSciNet  MATH  ADS  Google Scholar 

  • Kim, Y.-H., Kulik, S.P., Shih, Y.: Quantum teleportation of a polarization state with a complete Bell state measurement. Phys. Rev. Lett. 86(7), 1370 (2001)

    ADS  Google Scholar 

  • Lambert, N., Chen, Y.-N., Cheng, Y.-C., Li, C.-M., Chen, G.-Y., Nori, F.: Quantum biology. Nat. Phys. 9(1), 10–18 (2013)

    Google Scholar 

  • Li, B.-M., Hu, M.-L., Fan, H.: Nonlocal advantage of quantum coherence and entanglement of two spins under intrinsic decoherence. Chin. Phys. B 30(7), 070307 (2021)

    ADS  Google Scholar 

  • Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77(4), 042303 (2008)

    ADS  Google Scholar 

  • Maleki, Y.: Entanglement and decoherence in two-dimensional coherent state superpositions. Int. J. Theor. Phys. 56(3), 757–770 (2017)

    MATH  Google Scholar 

  • Malvezzi, A., Karpat, G., Çakmak, B., Fanchini, F., Debarba, T., Vianna, R.: Quantum correlations and coherence in spin-1 Heisenberg chains. Phys. Rev. B 93(18), 184428 (2016)

    ADS  Google Scholar 

  • Mansour, M., Dahbi, Z.: Entanglement of bipartite partly non-orthogonal-spin coherent states. Laser Phys. 30(8), 085201 (2020)

    ADS  Google Scholar 

  • Mansour, M., Dahbi, Z.: Quantum secret sharing protocol using maximally entangled multi-qudit states. Int. J. Theor. Phys. 59(12), 3876–3887 (2020)

    MathSciNet  MATH  Google Scholar 

  • Mansour, M., Oulouda, Y., Sbiri, A., Falaki, M.E.: Decay of negativity of randomized multiqubit mixed states. Laser Phys. 31(3), 035201 (2021)

    ADS  Google Scholar 

  • Melo-Luna, C.A., Susa, C.E., Ducuara, A.F., Barreiro, A., Reina, J.H.: Quantum locality in game strategy. Sci. Rep. 7(1), 1–11 (2017)

    Google Scholar 

  • Milburn, G.: Intrinsic decoherence in quantum mechanics. Phys. Rev. A 44(9), 5401 (1991)

    MathSciNet  ADS  Google Scholar 

  • Mofidnakhaei, F., Khastehdel Fumani, F., Mahdavifar, S., Vahedi, J.: Quantum correlations in anisotropic XY-spin chains in a transverse magnetic field. Phase Transit. 91(12), 1256–1267 (2018)

    Google Scholar 

  • Mohamed, A.-B.A., Abdel-Aty, A.-H., Qasymeh, M., Eleuch, H.: Non-local correlation dynamics in two-dimensional graphene. Sci. Rep. 12(1), 1–12 (2022)

    Google Scholar 

  • Mohamed, A.-B.A., Eleuch, H.: Quasi-probability information in a coupled two-qubit system interacting non-linearly with a coherent cavity under intrinsic decoherence. Sci. Rep. 10(1), 1–11 (2020)

    Google Scholar 

  • Mohamed, A.A., Eleuch, H.: Thermal local fisher information and quantum uncertainty in Heisenberg model. Phys. Scr. 97(9), 095105 (2022)

    ADS  Google Scholar 

  • Mohamed, A.B.A., Khedr, A.N., Haddadi, S., Rahman, A.U., Tammam, M., Pourkarimi, M.R.: Intrinsic decoherence effects on nonclassical correlations in a symmetric spin–orbit model. Result Phys. 39, 105693 (2022)

    Google Scholar 

  • Mohamed, A.-B.A., Rahman, A.U., Eleuch, H.: Measurement uncertainty, purity, and entanglement dynamics of maximally entangled two qubits interacting spatially with isolated cavities: intrinsic decoherence effect. Entropy 24(4), 545 (2022)

    MathSciNet  ADS  Google Scholar 

  • Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120(1), 91 (1960)

    ADS  Google Scholar 

  • Muthuganesan, R., Chandrasekar, V.: Intrinsic decoherence effects on measurement-induced nonlocality. Quantum Inf. Process. 20(1), 1–15 (2021)

    MathSciNet  MATH  Google Scholar 

  • Narasimhachar, V., Gour, G.: Low-temperature thermodynamics with quantum coherence. Nat. Commun. 6(1), 1–6 (2015)

    Google Scholar 

  • Naveena, P., Muthuganesan, R., Chandrasekar, V.: Effects of intrinsic decoherence on quantum correlations in a two superconducting charge qubit system. Physica A 592, 126852 (2022)

    MathSciNet  MATH  Google Scholar 

  • Nielsen, M.A., Chuang, I.: Quantum computation and quantum information (2002)

  • Obada, A.-S., Hessian, H.A., Mohamed, A., Hashem, M.: Influence of the phase damping for two-qubits system in the dispersive reservoir. Quantum Inf. Process. 12(5), 1947–1956 (2013)

    MATH  ADS  Google Scholar 

  • Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88(1), 017901 (2001)

    MATH  ADS  Google Scholar 

  • Oumennana, M., Dahbi, Z., Mansour, M., Khedif, Y.: Geometric measures of quantum correlations in a two-qubit heisenberg XXZ model under multiple interactions Effects. J. Russ. Laser Res. 43(5), 533–545 (2022)

    Google Scholar 

  • Oumennana, M., Rahman, A.U., Mansour, M.: Quantum coherence versus non-classical correlations in XXZ spin-chain under Dzyaloshinsky–Moriya (DM) and KSEA interactions. Appl. Phys. B 128(9), 1–13 (2022)

    Google Scholar 

  • Pan, F., Qiu, L., Liu, Z.: The complementarity relations of quantum coherence in quantum information processing. Sci. Rep. 7(1), 1–8 (2017)

    ADS  Google Scholar 

  • Pires, D.P., Silva, I.A., deAzevedo, E.R., Soares-Pinto, D.O., Filgueiras, J.G.: Coherence orders, decoherence, and quantum metrology. Phys. Rev. A 98(3), 032101 (2018)

    ADS  Google Scholar 

  • Ritz, T.: Quantum effects in biology: bird navigation. Procedia Chem. 3(1), 262–275 (2011)

    Google Scholar 

  • Schlosshauer, M.: Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys. 76(4), 1267 (2005)

    ADS  Google Scholar 

  • Schlosshauer, M.: Quantum decoherence. Phys. Rep. 831, 1–57 (2019)

    MathSciNet  ADS  Google Scholar 

  • Scholes, G.D.: Coherence in photosynthesis. Nat. Phys. 7(6), 448–449 (2011)

    Google Scholar 

  • Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Moriya’s anisotropic superexchange interaction, frustration, d dzyaloshinsky’s weak ferromagnetism,. Phys. Rev. Lett. 69(5), 836 (1992)

    ADS  Google Scholar 

  • Tan, K.C., Kwon, H., Park, C.-Y., Jeong, H.: Unified view of quantum correlations and quantum coherence. Phys. Rev. A 94(2), 022329 (2016)

    ADS  Google Scholar 

  • Wang, C.-Z., Li, C.-X., Nie, L.-Y., Li, J.-F.: Classical correlation and quantum discord mediated by cavity in two coupled qubits. J. Phys. B: At. Mol. Opt. Phys. 44(1), 015503 (2010)

    ADS  Google Scholar 

  • Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40(8), 4277 (1989)

    MATH  ADS  Google Scholar 

  • Wu, Y.-L., Deng, D.-L., Li, X., Sarma, S.D.: Intrinsic decoherence in isolated quantum systems. Phys. Rev. B 95(1), 014202 (2017)

    ADS  Google Scholar 

  • Xie, Y.-X., Liu, X.-Y.: Enhancing steered coherence in the Heisenberg model using Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. Laser Phys. Lett. 19(2), 025204 (2022)

    ADS  Google Scholar 

  • Yin, S., Liu, S., Song, J., Luan, H.: Markovian and non-Markovian dynamics of quantum coherence in the extended X X chain. Phys. Rev. A 106(3), 032220 (2022)

    ADS  Google Scholar 

  • Yuan, X., Zhou, H., Cao, Z., Ma, X.: Intrinsic randomness as a measure of quantum coherence. Phys. Rev. A 92(2), 022124 (2015)

    ADS  Google Scholar 

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Acknowledgements

Z. D expresses special thanks to the Abdus Salam International Centre for Theoretical Physics (ICTP) for the hospitality and for providing access to their research facilities during his visit, which helped accomplish some of this work. M. O acknowledges the financial support received from the National Center for Scientific and Technical Research (CNRST) under the Program of Excellence Grants for Research.

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Authors and Affiliations

  1. Lab of High Energy Physics-Modeling and Simulation, Faculty of Sciences, Mohammed V University in Rabat, 4 Avenue Ibn Battouta B.P., 1014 RP, Rabat, Morocco

    Zakaria Dahbi

  2. Laboratory of High Energy Physics and Condensed Matter, Department of Physics, Faculty of Sciences Ain Chock, Hassan II University, P.O. Box 5366, Maarif, 20100, Casablanca, Morocco

    Mansoura Oumennana & Mostafa Mansour

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  1. Zakaria Dahbi
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  2. Mansoura Oumennana
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  3. Mostafa Mansour
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ZD developed the theoretical formalism, performed the analytic calculations and performed the numerical simulations. MO contributed to writing the initial draft and discussion of the manuscript. MM supervised the project. All authors reviewed the final draft of the manuscript.

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Correspondence to Zakaria Dahbi.

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Dahbi, Z., Oumennana, M. & Mansour, M. Intrinsic decoherence effects on correlated coherence and quantum discord in XXZ Heisenberg model. Opt Quant Electron 55, 412 (2023). https://doi.org/10.1007/s11082-023-04604-3

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