Abstract
In this manuscript, we explore the characteristics of thermal entanglement and skew information correlations in a dipolar coupled-spins system subjected to the combined effect of Kaplan–Shekhtman–Entin–Wohlman–Aharony (KSEA) and Dzyaloshinsky–Moriya (DM) interactions in the presence of an external homogenous magnetic field. We employ logarithmic negativity (LN) to characterize the degree of entanglement. Under the thermal reservoir effect, uncertainty-induced non-locality (UIN) and local quantum uncertainty (LQU) are both utilized to evaluate skew information correlations in the investigated system. The variations of the logarithmic negativity and skew information quantifiers are studied in terms of the equilibrium temperature, the dipolar coupling strengths among the two linked spins, DM and KSEA coupling parameters, and the intensity of the homogeneous magnetic field. The findings reveal that the non-classical correlations seen between two linked spins may be adjusted by changing the dipolar interaction coupling strengths between the coupled spins, the intensity of KSEA interaction and the strength of the homogeneous magnetic field B. In addition, our findings demonstrate that the skew information correlations tolerate thermal noise better than entanglement and that LQU and UIN quantifiers disclose more non-classical correlations beyond the LN in the dipole–dipole two-spin system. Our findings also confirm that the UIN is more resistant than the LQU against rising temperatures.
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References
Bennett, C. H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. arXiv:2003.06557 (2020)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)
Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656 (1996)
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, 1895 (1993)
Bouwmeester, D., Pan, J.-W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575–579 (1997)
Nielsen, M., Chuang, I.: Quantum computation and quantum information. Phys. Today 54(2), 60 (2000)
Barenco, A., Deutsch, D., Ekert, A., Jozsa, R.: Conditional quantum dynamics and logic gates. Phys. Rev. Lett. 74, 4083 (1995)
Deutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. R. Soc. London. A Math. Phys. Sci. 400, 97–117 (1985)
Mansour, M., Dahbi, Z.: Quantum secret sharing protocol using maximally entangled multi-qudit states. Int. J. Theo. Phys. 59, 3876–3887 (2020)
Bennett, Charles H., et al.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)
Vallone, G., Marangon, D.G., Tomasin, M., Villoresi, P.: Quantum randomness certified by the uncertainty principle. Phy. Rev. A 90, 052327 (2014)
Mansour, M., Dahbi, Z.: Entanglement of bipartite partly non-orthogonal-spin coherent states. Laser Phys. 30, 085201 (2020)
Abdel-Aty, A.H., Khedr, A.N., Saddeek, Y.B., Youssef, A.A.: Thermal entanglement in quantum annealing processor. Int. J. Quant. Inf. 16, 1850006 (2018)
Mansour, M., Daoud, M., Dahbi, Z.: Randomized entangled mixed states from phase states. Int. J. Theo. Phys. 59, 895–907 (2020)
Mansour, M., Dahbi, Z., Essakhi, M., Salah, A.: Quantum correlations through spin coherent states. Int. J. Theo. Phys. 60, 2156–2174 (2021)
Wootters, W.K.: Entanglement of formation and concurrence. Quantum Inf. Comput. 1, 27–44 (2001)
Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)
Plenio, M.B.: Logarithmic negativity: a full entanglement monotone that is not convex. Phys. Rev. Lett. 95, 090503 (2005)
Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)
Horodecki, M., Horodecki, P., Horodecki, R.: On the necessary and sufficient conditions for separability of mixed quantum states. arXiv preprint arXiv:quant-ph/9605038 (1996)
Lee, S., Chi, D.P., Oh, S.D., Kim, J.: Convex-roof extended negativity as an entanglement measure for bipartite quantum systems. Phys. Rev. A 68, 062304 (2003)
Mansour, M., Oulouda, Y., Sbiri, A., El Falaki, M.: Decay of negativity of randomized multi-qubit mixed states. Laser Phys. 31, 035201 (2021)
Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)
Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A: Math. Gen. 34, 6899 (2001)
Luo, S.: Quantum discord for two-qubit systems. Phys-ical Review A 77(4), 042303 (2008)
Dakić, B., Vedral, V., Brukner, Č: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)
Luo, S., Fu, S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010)
Hassan, A.S.M., Lari, B., Joag, P.S.: Tight lower bound to the geometric measure of quantum discord. Phys. Rev. A 85, 024302 (2012)
Ciccarello, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. 16, 013038 (2014)
Wigner, E.P., Yanase, M.M.: Information contents of distributions. Proc. Natl. Acad. Sci. 49, 910–918 (1963)
Luo, S.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91, 180403 (2003)
Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)
Sbiri, A., Mansour, M., Oulouda, Y.: Local quantum uncertainty versus negativity through Gisin states. Int. J. Quantum Inf. 19, 05 (2021)
Essakhi, M., Khedif, Y., Mansour, M., et al.: Non-classical correlations in multipartite generalized coherent states. Braz. J. Phys. 52, 124 (2022)
Sbiri, A., Oumennana, M., Mansour, M.: Thermal quantum correlations in a two-qubit Heisenberg model under Calogero–Moser and Dzyaloshinsky–Moriya interactions. Mod. Phys. Lett. B 36, 2150618 (2022)
Yang, C., Guo, Y.N., Peng, H.P., Lu, Y.B.: Dynamics of local quantum uncertainty for a two-qubit system under dephasing noise. Laser Phys. 30, 015203 (2019)
Khedr, A.N., Homid, A.H., Mohamed, A.B.A., Abdel-Aty, A.H., Eleuch, H., Tammam, M., Abdel-Aty, M.: Robust thermal correlations induced by spin-orbit interactions. Results Phys. 38, 105619 (2022)
Elghaayda, S., Dahbi, Z., Mansour, M.: Local quantum uncertainty and local quantum Fisher information in two-coupled double quantum dots. Opt. Quantum Electron. 54, 419 (2022)
Dahbi, Z., Ur, Rahman A., Mansour, M.: Skew information correlations and local quantum Fisher information in two gravitational cat states. Physica A 609, 128333 (2023)
Wu, S.X., Zhang, J., Yu, C.S., Song, H.S.: Uncertainty-induced quantum nonlocality. Phys. Lett. A 378, 344–347 (2014)
Luo, S., Fu, S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)
Hu, M.L., Fan, H.: Measurement-induced nonlocality based on the trace norm. New J. Phys. 17, 033004 (2015)
Kuznetsova, E.I., Yurischev, M.A.: Quantum discord in spin systems with dipole-dipole interaction. Quantum Inf. Process. 12, 3587–3605 (2013)
Furman, G.B., Meerovich, V.M., Sokolovsky, V.L.: Entanglement in dipolar coupling spin system in equilibrium state. Quantum Inf. Process. 11, 1603–1617 (2012)
Hu, Z.D., Wang, J., Zhang, Y., Zhang, Y.Q.: Sudden transitions of trace distance discord of dipole-dipole coupled two qubits. Int. J. Mod. Phys. B 29, 1550138 (2015)
Peter, D., Müller, S., Wessel, S., Büchler, H.P.: Anomalous behavior of spin systems with dipolar interactions. Phys. Rev. Lett. 109, 025303 (2012)
Martinis, J.M., Cooper, K.B., McDermott, R., Steffen, M., Ansmann, M., Osborn, K.D., Clare, C.Y.: Decoherence in Josephson qubits from dielectric loss. Phys. Rev. Lett. 95, 210503 (2005)
Zhou, Y.L., Ou, B.Q., Wu, W.: Quantum simulating the frustrated Heisenberg model in a molecular dipolar crystal. Phys. Lett. A 379, 2569–2576 (2015)
Rabl, P., Zoller, P.: Molecular dipolar crystals as high-fidelity quantum memory for hybrid quantum computing. Phys. Rev. A 76, 042308 (2007)
Büchler, H.P., Micheli, A., Zoller, P.: Three-body interactions with cold polar molecules. Nat. Phys. 3, 726–731 (2007)
Rajapakse, R.M., Bragdon, T., Rey, A.M., Calarco, T., Yelin, S.F.: Single-photon nonlinearities using arrays of cold polar molecules. Phys. Rev. A 80, 013810 (2009)
Carr, L.D., DeMille, D., Krems, R.V., Ye, J.: Cold and ultracold molecules: science, technology and applications. New J. Phys. 11, 055049 (2009)
Gorshkov, A.V., Manmana, S.R., Chen, G., Ye, J., Demler, E., Lukin, M.D., Rey, A.M.: Tunable superfluidity and quantum magnetism with ultracold polar molecules. Phys. Rev. Lett. 107, 115301 (2011)
Mohammed, A.R., Ahmed, A.H., El-Shahat, T.M., Metwally, N.: Quantum steering over an entangled network that is generated via Dipolar interaction. Phys. A: Stat. Mech. Appl. 584, 126380 (2021)
Dzyaloshinsky, I.: A thermodynamic theory of “weak’’ ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958)
Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91 (1960)
Khedr, A.N., Mohamed, A.B.A., Abdel-Aty, A.H., Tammam, M., Abdel-Aty, M., Eleuch, H.: Entropic uncertainty for two coupled dipole spins using quantum memory under the Dzyaloshinskii–Moriya interaction. Entropy 23, 1595 (2021)
Kaplan, T.A.: Single-band Hubbard model with spin-orbit coupling. Z. Phys. B Cond. Mat. 49, 313–317 (1983)
Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Moriya’s anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism. Phys. Rev. Lett. 69, 836 (1992)
Shekhtman, L., Aharony, A., Entin-Wohlman, O.: Bond-dependent symmetric and antisymmetric superexchange interactions in La\(_2\)CuO\(_4\). Phys. Rev. B 47, 174 (1993)
Zheludev, A., Maslov, S., Zaliznyak, I., Regnault, L. P., Masuda, T., Uchinokura, K., Shirane, G.: Experimental evidence for Shekhtman–Entin–Wohlman–Aharony (SEA) interactions in Ba\(_2\)CuGe\(_2\)O\(_7\). arXiv preprint arXiv:cond-mat/9805236 (1998)
Yildirim, T., Harris, A.B., Aharony, A., Entin-Wohlman, O.: Anisotropic spin Hamiltonians due to spin-orbit and Coulomb exchange interactions. Phys. Rev. B 52, 10239 (1995)
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. Results Phys. 39, 105693 (2022)
Tsukada, I., Sun, X.F., Komiya, S., Lavrov, A.N., Ando, Y.: Significant suppression of weak ferromagnetism in (La\(_1.8\)Eu\(_0.2\))CuO\(_4\). Phys. Rev. B 67, 224401 (2003)
Lumsden, M.D., Sales, B.C., Mandrus, D., Nagler, S.E., Thompson, J.R.: Weak ferromagnetism and field-induced spin reorientation in K\(_2\)V\(_3\)O\(_8\). Phys. Rev. Lett. 86, 159 (2001)
Zheludev, A., Maslov, S., Shirane, G., Tsukada, I., Masuda, T., Uchinokura, K., Zaliznyak, I., Erwin, R., Regnault, L.P.: Magnetic anisotropy and low-energy spin waves in the Dzyaloshinskii–Moriya spiral magnet Ba\(_2\)CuGe\(_2\)O\(_7\) Phys. Rev. B 59, 11432 (1999)
Mühlbauer, S., Brandl, G., Månsson, M., Garst, M.: Formation of incommensurate long-range magnetic order in the Dzyaloshinskii–Moriya antiferromagnet Ba\(_2\)CuGe\(_2\)O\(_7\) studied by neutron diffraction. Phys. Rev. B 96, 134409 (2017)
Emori, S., Bauer, U., Ahn, S.M., Martinez, E., Beach, G.S.: Current-driven dynamics of chiral ferromagnetic domain walls. Nat. Mater. 12, 611–616 (2013)
Yu, X.Z., Kanazawa, N., Zhang, W.Z., Nagai, T., Hara, T., Kimoto, K., Tokura, Y.: Skyrmion flow near room temperature in an ultralow current density. Nat. Commun. 3, 1–6 (2012)
Liu, B.Q., Shao, B., Li, J.G., Zou, J., Wu, L.A.: Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii–Moriya interaction. Phys. Rev. A 83, 052112 (2011)
Yurischev, M.A.: On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. Quantum Inf. Process. 19, 1–20 (2020)
Oumennana, M., Rahman, A.U., Mansour, M.: Quantum coherence versus non-classical correlations in XXZ spin-chain under Dzyaloshinsky–Moriya (DM) and KSEA interactions. App. Phys. B 128, 1–13 (2022)
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, 533–545 (2022)
Hashem, M., Mohamed, A.B.A., Haddadi, S., et al.: Bell nonlocality, entanglement, and entropic uncertainty in a Heisenberg model under intrinsic decoherence: DM and KSEA interplay effects. Appl. Phys. B 128, 87 (2022)
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, 2150209 (2021)
Fedorova, A.V., Yurischev, M.A.: Behavior of quantum discord, local quantum uncertainty, and local quantum Fisher information in two-spin-1/2 Heisenberg chain with DM and KSEA interactions. Quantum Inf. Process. 21, 92 (2022)
Horodecki, M., Horodecki, P., Horodecki, R.: Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps. Phys. Lett. A 283, 1–7 (2001)
Reis, M.S.: Foundations of Magnetism. Elsevier, New York (2013)
Li, D.C., Cao, Z.L.: Entanglement in the anisotropic Heisenberg XYZ model with different Dzyaloshinskii–Moriya interaction and inhomogeneous magnetic field. Eur. Phys. J. D 50, 207–214 (2008)
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Elghaayda, S., Khedr, A.N., Tammam, M. et al. Quantum entanglement versus skew information correlations in dipole–dipole system under KSEA and DM interactions. Quantum Inf Process 22, 117 (2023). https://doi.org/10.1007/s11128-023-03866-w
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DOI: https://doi.org/10.1007/s11128-023-03866-w