JQIS  Vol.4 No.4 , December 2014
Tailoring Quantum Correlations of a Coupled Central Two Qubits Soaked in a Finite Temperature Antiferromagnetic Environment with Frequency Gap
Abstract: We revisit the quantum features of an anti-ferromagnetic (AF) spin environment at finite temperature with gap in its frequency spectrum, on the dynamics quantum correlations of a coupled central two qubits system with Dzyaloshinskii-Moriya (DM) interaction, prepared in two entangled Bell states. Using entanglement and quantum discord as quantum meters of decoherence, the prepared entangled states are classified as robust or fragile relative to the degree of information leakage to the AF environment. By tailoring the size of the frequency gap, anisotropy field strength and induced field, due to system AF spin environment coupling, size of the AF environment and DM interaction parameter, a decoherence-free sub-space can be accessed for efficient execution of quantum protocols encoded in the entangled states.
Cite this paper: Fai, L. , Afuoti, N. , Fouokeng, G. , Kuetche, J. and Tchoffo, M. (2014) Tailoring Quantum Correlations of a Coupled Central Two Qubits Soaked in a Finite Temperature Antiferromagnetic Environment with Frequency Gap. Journal of Quantum Information Science, 4, 201-213. doi: 10.4236/jqis.2014.44019.

[1]   Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge.

[2]   Datta, A., Shaji, A. and Caves, C.M. (2008) Quantum Discord and the Power of One Qubit. Physical Review Letters, 100, Article ID: 050502.

[3]   Fouokeng, G.C., Tchoffo, M., Tendong, E. and Fai, L.C. (2014) Dzyaloshinskii-Moriya Interactions Effects on the Entanglement Dynamics of a Two Qubitxxz Spin System in Non-Markovian Environment. arXiv:1405.7009v1 [quant-ph]

[4]   Benedetti, C., Buscemi, F., Bordone, P. and Paris, M.G.A. (2012) Effects of Classical Environmental Noise on Entanglement and Quantum Discord Dynamics. International Journal of Quantum Information, 10, Article ID: 1241005.

[5]   Cai, J.M., et al. (2012) Robust Dynamical Decoupling with Concatenated Continuous Driving. New Journal of Physics, 14, 16.

[6]   Klinovaja, J., Stepanenko, D. and Halperin, B.I. (2012) Exchange-Based CNOT Gates for Singlet-Triplet Qubits with Spin Orbit Interaction. Physical Review B, 86, Article ID: 085423.

[7]   Feng, Z.-B., Zhang, C.-L. and Zhou, Y.-Q. (2014) Robust Quantum Computing in Decoherence-Free Subspaces with Double-Dot Spin Qubits. Communications in Theoretical Physics, 61, 181.

[8]   Campagnano, G., Hamma, A. and Weiss, U. (2010) Entanglement Dynamics of Coupled Qubits and a Semi-Decoherence Free Subspace. Physical Letters A, 374, 416-423.

[9]   Bi, Q., Guo, L. and Ruda, H.E. (2010) Quantum Computing in Decoherence Free Subspace Constructed by Triangulation. Advances in Mathematical Physics, 2010, Article ID: 365653.

[10]   Brouard, S. and Plata, J., (2004) Decoherence of Trapped-Ion Internal and Vibrational Modes: The Effect of Fluctuating Magnetic Fields. Physical Review A, 70, Article ID: 013413.

[11]   Tchoffo, M., Fouokeng, G.C., Massou, S., Afuoti, N.E., Nsangou, I., Fai, L.C., Tchouadeu, A.G. and Kenne, J.P. (2012) Effect of the Variable B-Field on the Dynamic of a Central Electron Spin Coupled to an Anti-Ferromagnetic Qubit Bath. World Journal of Condensed Matter Physics, 2, 246-256.

[12]   Fouokeng, G.C., Tchoffo, M., Moussiliou, S., Ngana Kuetche, J.C., Fai, L.C. and Siaka, M. (2014) Effect of Noise on the Decoherence of a Central Electron Spin Coupled to an Antiferromagnetic Spin Bath. Advances in Condensed Matter Physics, 2014, Article ID: 526205.

[13]   Tchoffo, M., Fouokeng, G.C., Fai, L.C. and Ateuafack, M.E. (2013) Thermodynamic Properties and Decoherence of a Central Electron Spin of Atom Coupled to an Anti-Ferromagnetic Spin Bath. Journal of Quantum Information Science, 3, 10-15.

[14]   Wu, L.A., Yu, C.X. and Segal, D. (2013) Exact Dynamics of Interacting Qubits in a Thermal Environment Results beyond the Weak Coupling Limit. New Journal of Physics, 15, Article ID: 023044.

[15]   Tomotaka, K. and Naomichi, H. (2011) Maximization of Thermal Entanglement of Arbitrarily Interacting Two Qubits. Physical Review A, 83, Article ID: 062311.

[16]   Jing, N., Cheng, W.L. and Xi, Y.X. (2009) Disentanglement of Two Qubits Coupled to an XY Spin Chain at Finite Temperature. Communications in Theoretical Physics, 51, 815.

[17]   Dzyaloshinsky, I. (1958) A Thermodynamic Theory of Weak Ferromagnetism of Antiferromagnetics. Journal of Physics and Chemistry of Solids, 4, 241-255.

[18]   You, W.L. and Dong, Y.L. (2010) The Entanglement Dynamics of Interacting Qubits Embedded in a Spin Environment with Dzyaloshinsky Moriya Term. The European Physical Journal D, 57, 439-445.

[19]   Tao, C., Xia, H.Y.S., Jia, C., Xing, L.J., Bing, L.J. and Kun, LT. (2010) Entanglement Evolution in an Anisotropic Two-Qubits Heisenberg XYZ Model with Dzyaloshinskii Moriya Interaction. Chinese Physics B, 19, Article ID: 050302.

[20]   Mozyrsky, D. and Privman, V. (1998) Adiabatic Decoherence. Journal of Statistical Physics, 91, 787-799.

[21]   Yuan, X.Z., Goan, H.S. and Zhu, K.-D. (2007) Influence of an External Magnetic Field on the Decoherence of a Central Spin Coupled to an Antiferromagnetic Environment. New Journal of Physics, 9, 219.

[22]   Wootters, W.K. (1998) Entanglement of Formation of an Arbitrary State of Two Qubits. Physical Review Letters, 80, 2245-2228.

[23]   Ollivier, H. and Zurek, W.H. (2002) A Measure of the Quantumness of Correlations. Physical Review Letters, 88, Article ID: 017901.

[24]   Ali, M., Rau, A.R.P. and Alber, G. (2010) Quantum Discord for Two-Qubit X States. Physical Review A, 81, Article ID: 042105.

[25]   Luo, S. (2008) Quantum Discord for Two-Qubit Systems. Physical Review A, 77, Article ID: 042303.

[26]   Luo, S. and Fu, S. (2010) Geometric Measure of Quantum Discord. Physical Review A, 82, Article ID: 034302.

[27]   Berrada, K., Eleuch, H. and Hassouni, Y. (2011) Asymptotic Dynamics of Quantum Discord in Open Quantum Systems. Journal of Physics B: Atomic, Molecular and Optical Physics, 44, Article ID: 145503.