Abstract
We investigate the influence of intrinsic decoherence on the quantum correlations in a two-qubit Heisenberg XYZ spin chain in the presence of the z-component of Dzyaloshinskii–Moriya interaction by employing logarithmic negativity and trace distance discord as reliable quantum correlation quantifiers. We highlight the dynamics behaviours of suggested quantifiers for a system initially prepared in the extended Werner-like state. For an initial separable state, it is found that the robustness and the generation of the quantum correlations depend on the physical parameters. While considering the entangled state as an initial state, the results show that despite the phase decoherence, all the correlations reach their steady state values after exhibiting some oscillations. We reveal that TDD is relatively more robust against the intrinsic decoherence compared to the logarithmic negativity and increasing the intrinsic decoherence rate leads to a drastic decrease of the quantum correlations between the two qubits.
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References
Abdel-Aty, M.: New features of total correlations in coupled Josephson charge qubits with intrinsic decoherence. Phys. Lett. A 372, 3719 (2008)
Asoudeh, M., Karimipour, V.: Thermal entanglement of spins in an inhomogeneous magnetic field. Phys. Rev. A 71, 022308 (2005)
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)
Bloch, F.: Nuclear Induction. Phys. Rev. 70, 460 (1946)
Bose, S.: Quantum Communication through an Unmodulated Spin Chain. Phys. Rev. Lett. 91, 207901 (2003)
Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575 (1997)
Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869 (1998)
Buz̆ek, V., Konôpka, M.: Dynamics of open systems governed by the Milburn equation. Phys. Rev. A 58, 1735 (1998)
Caves, C.M., Milburn, G.J.: Quantum-mechanical model for continuous position measurements. Phys. Rev. D 36, 5543 (1987)
Ciccarello, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. New J. Phys. 16, 013038 (2014)
Dakić, B., Vedral, V., Brukner, Č: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)
Datta, A., Vidal, G.: Role of entanglement and correlations in mixed-state quantum computation. Phys. Rev. A 75, 042310 (2007)
Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)
Debarba, T., Maciel, T.O., Vianna, R.O.: Witnessed entanglement and the geometric measure of quantum discord. Phys. Rev A 86, 024302 (2012)
Dehghani, A., Mojaveri, B., Vaez, M.: Entanglement dynamics of two coupled spins interacting with an adjustable spin bath: effect of an exponential variable magnetic field. Quant. Info. Proc. 19, 306 (2020)
Diosi, L.: Models for universal reduction of macroscopic quantum fluctuations. Phys. Rev. A 40, 1165 (1989)
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
Ellis, J., Mohanty, S., Nanopaulos, D.: Quantum gravity and the collapse of the wavefunction. Phys. Lett. B 221, 113 (1989)
Fano, U.: Pairs of two-level systems. Rev. Mod. Phys. 55, 855 (1983)
Ghirardi, G.C., Rimini, A., Weber, T.: Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470 (1986)
Ghirardi, G.C., Pearle, P., Rimini, A.: Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Phys. Rev. A 42, 78 (1990)
Guo, J.L., Song, H.S.: Effects of inhomogeneous magnetic field on entanglement and teleportation in a two-qubit Heisenberg XXZ chain with intrinsic decoherence. Phys. Scr. 78, 045002 (2008)
Gühne, O., Tóth, G.: Entanglement detection. Phys. Rep. 474, 1 (2009)
Habiballah, N., Khedif, Y., Daoud, M.: Local quantum uncertainty in XYZ Heisenberg spin models with Dzyaloshinski-Moriya interaction. Eur. Phys. J. D 72, 154 (2018)
He, Z., Xiong, Z., Zhang, Y.: Influence of Intrinsic Decoherence on Quantum Teleportation via Two-Qubit Heisenberg (XYZ) Chain. Phys. Lett. A 354, 79 (2006)
Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A: Math. Gen. 34, 6899 (2001)
Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Khedif, Y., Daoud, M.: Local quantum uncertainty and trace distance discord dynamics for two-qubit X states embedded in non-Markovian environment. Int. J. Mod. Phys. B 32, 1850218 (2018)
Khedif, Y., Daoud, M.: Pairwise nonclassical correlations for superposition of Dicke states via local quantum uncertainty and trace distance discord. Quantum Inf. Process. 18, 45 (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 (2021)
Khedif, Y., Daoud, M., Sayouty, E.H.: Thermal quantum correlations in a two-qubit Heisenberg XXZ spin-\(\frac{1}{2}\) chain under an inhomogeneous magnetic field. Phys. Scr. 94, 125106 (2019)
Khedif, Y., Errehymy, A., Daoud, M.: On the thermal nonclassical correlations in a two-spin XYZ Heisenberg model with Dzyaloshinskii-Moriya interaction. Eur. Phys. J. Plus 136, 336 (2021)
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)
Kuang, L.M., Chen, X., Ge, M.L.: Influence of intrinsic decoherence on nonclassical effects in the multiphoton Jaynes-Cummings model. Phys. Rev. A 52, 1857 (1995)
Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008)
Liang, Q., An-Min, W., Xiao-San, M.: Effect of Intrinsic Decoherence of Milburn’s Model on Entanglement of Two-Qutrit States. Commun. Theor. Phys. 49, 516 (2008)
Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77(042303), 022301 (2008)
Mansour, M., Daoud, M.: Entangled thermal mixed states for multi-qubit systems. Mod. Phys. Lett. B 33, 1950254 (2019)
Mansour, M., Haddadi, S.: Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states. Mod. Phys. Lett. A 36, 2150010 (2021)
Massashi, B., Sachiko, K., Fumiaki, S.: Quantum master equation approach to dynamical suppression of decoherence. J. Phys. B: At. Mol. Opt. Phys. 40, 2641 (2007)
Milburn, G.J.: Intrinsic decoherence in quantum mechanics. Phys. Rev. A 44, 5401 (1991)
Mojaveri, B., Dehghani, A., Fasihi, M.A., Mohammadpour, T.: Thermal Entanglement Between Two Two-Level Atoms in a Two-Photon Jaynes-Cummings Model with an Added Kerr Medium. Int. J. Theor. Phys. 57, 3396 (2018)
Mojaveri, B., Dehghani, A., Fasihi, M.A., Mohammadpour, T.: Ground state and thermal entanglement between two two-level atoms interacting with a nondegenerate parametric amplifier: Different sub-spaces. Int. J. Mod. Phys. B 33, 1950035 (2019)
Montealegre, J.D., Paula, F.M., Saguia, A., Sarandy, M.S.: One-norm geometric quantum discord under decoherence. Phys. Rev. A 87, 042115 (2013)
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 (2001)
Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten \(1\)-norm. Phys. Rev. A 87, 064101 (2013)
Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)
Plenio, M.B.: Logarithmic Negativity: A Full Entanglement Monotone That is not Convex. Phys. Rev. Lett. 95, 090503 (2005)
Plenio, M.B., Knight, P.L.: Decoherence limits to quantum computation using trapped ions. Proc. Roy. Soc. Lond. A 453, 2017 (1997)
Rigolin, G.: Thermal entanglement in the two-qubit heisenberg XYZ model. Int. J. Quantum Inf. 14, 393 (2004)
Sbiri, A., Mansour, M., Oulouda, Y.: Local quantum uncertainty versus negativity through Gisin states. Int. J. Quantum Inf. 19, 2150023 (2021)
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 (2022)
Schrödinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555 (1935)
Vedral, V.: The role of relative entropy in quantum information theory. Rev. Mod. Phys. 74, 197 (2002)
Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)
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Essakhi, M., Khedif, Y., Mansour, M. et al. Intrinsic decoherence effects on quantum correlations dynamics. Opt Quant Electron 54, 103 (2022). https://doi.org/10.1007/s11082-021-03463-0
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DOI: https://doi.org/10.1007/s11082-021-03463-0