Abstract
We considered the two-qubit Heisenberg XXZ spin chain in the presence of Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions in thermal equilibrium. As discord-type quantifiers of thermal non-classical correlations, we used trace distance discord and local quantum uncertainty. Depending on the thermal state of the system considered, the explicit analytical expressions of the suggested quantifiers are derived and their behaviors with respect to the various parameters of the system are examined. The results obtained showed that the Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions considerably improve the quantum correlations contained in the bipartite system while the temperature tends to decrease their quantity.
Similar content being viewed by others
References
Abd-Rabboul, M.Y., Khalil, E.M., Abdel-Khalek, S., Al-Barakaty, A., Abu-Zinadah, H.: Quantum fisher information of a teleported state in Heisenberg XYZ chain with magnetic field and Kaplan–Shekhtman–Entin–Wohlman–Aharony interaction. IEEE Access 9, 51325–51331 (2021)
Ait Chlih, A., Habiballah, N., Nassik, M.: Dynamics of quantum correlations under intrinsic decoherence in a Heisenberg spin chain model with Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 20, 92–105 (2021)
Asoudeh, M., Karimipour, V.: Thermal entanglement of spins in an inhomogeneous magnetic field. Phys. Rev. A 71, 022308–022313 (2005)
Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)
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, 1895–1899 (1993)
Bloch, F.: Nuclear Induction. Phys. Rev. 70, 460–474 (1946)
Ciccarello, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. 16, 013038–013060 (2014)
Dakić, B., Vedral, V., Brukner, Č: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502–190505 (2010)
Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502–050505 (2008)
Debarba, T., Maciel, T.O., Vianna, R.O.: Reply to Comment on ‘Witnessed entanglement and the geometric measure of quantum discord’. Phys. Rev. A 86, 046301 (2013)
Essakhi, M., Khedif, Y., Mansour, M., Daoud, M.: Intrinsic decoherence effects on quantum correlations dynamics. Opt. Quant. Electron. 54, 103–117 (2022)
Fano, U.: Pairs of two-level systems. Rev. Mod. Phys. 55, 855–874 (1983)
Ferraro, A., Aolita, L., Cavalcanti, D., Cucchietti, F.M., Acín, A.: Almost all quantum states have non classical correlations. Phys. Rev. A 81, 052318–052323 (2010)
Girolami, D., Tufarelli, T., Adesso, G.: Characterizing non classical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402–240406 (2013)
Guo, J.-L., Mi, Y.-J., Zhang, J., Song, H.-S.: Thermal quantum discord of spins in an inhomogeneous magnetic field. J. Phys. B At. Mol. Opt. Phys. 44, 065504–065509 (2011)
Guo, Y.-N., Peng, H.-P., Tian, Q.-L., Tan, Z.-G., Chen, Y.: Local quantum uncertainty in a two-qubit Heisenberg spin chain with intrinsic decoherence. Phys. Scr. 96, 075101–07510 (2021)
Habiballah, N., Khedif, Y., Daoud, M.: Local quantum uncertainty in XYZ Heisenberg spin models with Dzyaloshinskii–Moriya interaction. Eur. Phys. J. D 72, 154–161 (2018)
Hashem, M., Mohamed, A.-B.A., Haddadi, S., Khedif, Y., Pourkarimi, M.R., Daoud, M.: Bell non locality, entanglement, and entropic uncertainty in a Heisenberg model under intrinsic decoherence: DM and KSEA interplay effects. Appl. Phys. B 128, 87–96 (2022)
Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. Gen. 34, 6899–6905 (2001)
Horodecki, M., Oppenheim, J., Winter, A.: Quantum information can be negative. Nature 436, 673–676 (2005)
Horodecki, M., Oppenheim, J., Winter, A.: Quantum state merging and negative information. Commun. Math. Phys. 269, 107–136 (2007)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)
Khedif, Y., Daoud, M.: Pairwise non classical correlations for superposition of Dicke states via local quantum uncertainty and trace distance discord. Quantum Inf. Process. 18, 45–65 (2019)
Khedif, Y., Daoud, M.: Thermal quantum correlations in the two-qubit Heisenberg XYZ spin chain with Dzyaloshinskii–Moriya interaction. Mod. Phys. Lett. A 36, 2150074–2150088 (2021)
Khedif, Y., Daoud, M., Sayouty, E.H.: Thermal quantum correlations in a two-qubit Heisenberg XXZ spin-1/2 chain under an inhomogeneous magnetic field. Phys. Scr. 94, 125106–125118 (2019)
Khedif, Y., Errehymy, A., Daoud, M.: On the thermal non classical correlations in a two-spin XYZ Heisenberg model with Dzyaloshinskii–Moriya interaction. Eur. Phys. J. Plus 136, 336–348 (2021a)
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, 2150209–2150224 (2021b)
Luo, S.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91, 180403-180406 (2003)
Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301–022305 (2008)
Ming, F., Wang, D., Shi, W.-N., Huang, A.-J., Sun, W.-Y., Ye, L.: Entropic uncertainty relations in the Heisenberg XXZ model and its controlling via filtering operations. Quantum Inf. Process. 17, 89–105 (2018a)
Ming, F., Wang, D., Shi, W.-N., Huang, A.-J., Du, M.-M., Sun, W.-Y., Ye, L.: Exploring uncertainty relation and its connection with coherence under the Heisenberg spin model with the Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 18, 267–282 (2018b)
Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655–1707 (2012)
Montealegre, J.D., Paula, F.M., Saguia, A., Sarandy, M.S.: One-norm geometric quantum discord under decoherence. Phys. Rev. A 87, 042115–042120 (2013)
Moriya, T.: New mechanism of anisotropic super exchange interaction. Phys. Rev. Lett. 4, 228–230 (1960a)
Moriya, T.: Anisotropic super exchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960b)
Muthuganesan, R., Chandrasekar, V.K.: Intrinsic decoherence effects on measurement-induced non locality. Quantum Inf. Process. 20, 46–60 (2021)
Najarbashi, G., Seifi, B.: Quantum phase transition in the Dzyaloshinskii–Moriya interaction with inhomogeneous magnetic field: geometric approach. Quantum Inf. Process. 16, 40–55 (2017)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901–017904 (2001)
Park, D.: Thermal entanglement and thermal discord in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions. Quantum Inf. Process. 18, 172–195 (2019)
Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten \(1\)-norm. Phys. Rev. A 87, 064101–064104 (2013)
Rana, S., Parashar, P.: Comment on “Witnessed entanglement and the geometric measure of quantum discord’’. Phys. Rev. A 87, 016301–016302 (2013)
Rigolin, G.: Thermal entanglement in the two-qubit Heisenberg XYZ model. Int. J. Quantum Inf. 14, 393-405 (2004)
Sha, Y.-T., Wang, Y., Sun, Z.-H., Hou, X.-W.: Thermal quantum coherence and correlation in the extended XY spin chain. Ann. Phys. 392, 229–241 (2018)
Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Moriya’s anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism. Phys. Rev. Lett. 69, 836–839 (1992)
Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Bond-dependent symmetric and antisymmetric super exchange interactions in La\(_2\)CuO\(_4\). Phys. Rev. B 47, 174–182 (1993)
Shi, W.-N., Ming, F., Wang, D., Ye, L.: Entropic uncertainty relations in the spin-\(1\) Heisenberg model. Quantum Inf. Process. 18, 70–86 (2019)
Sun, Y., Chen, Y., Chen, H.: Thermal entanglement in the two-qubit Heisenberg XY model under a nonuniform external magnetic field. Phys. Rev. A 68, 044301–044304 (2003)
Wang, S., Li, H., Lu, X., Long, G.-L.: Closed form of local quantum uncertainty and a sudden change of quantum correlations. https://arxiv.org/abs/1307.0576v2
Wang, X.: Entanglement in the quantum Heisenberg XY model. Phys. Rev. A 64, 012313–012319 (2001)
Werlang, T., Rigolin, G.: Thermal and magnetic quantum discord in Heisenberg models. Phys. Rev. A 81, 044101–044104 (2010)
Wigner, E.P., Yanasse, M.M.: Information contents of distributions. Proc. Natl. Acad. Sci. U.S.A. 49, 910–918 (1963)
Yang, Y.-Y., Sun, W.-Y., Shi, W.-N., Ming, F., Wang, D., Ye, L.: Dynamical characteristic of measurement uncertainty under Heisenberg spin models with Dzyaloshinskii–Moriya interactions. Front. Phys. 14, 31601–31609 (2019)
Yurischev, M.A.: On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. Quantum Inf. Process. 19, 336–355 (2020)
Zhang, G.-F., Li, S.-S.: Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field. Phys. Rev. A 72, 034302–034305 (2005)
Funding
Not applicable.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Aroui, A.E., Khedif, Y., Habiballah, N. et al. Characterizing the thermal quantum correlations in a two-qubit Heisenberg XXZ spin-\(\frac{1}{2}\) chain under Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. Opt Quant Electron 54, 694 (2022). https://doi.org/10.1007/s11082-022-04042-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-022-04042-7