Study of Decoherence on the Teleportation Algorithm in a Chain of Three Nuclear Spins System


We make a numerical study of decoherence on the teleportation algorithm implemented in a linear chain of three nuclear spins system. We study different types of environments, and we determine the associated decoherence time as a function of the dissipative parameter. We found that the dissipation parameter to get a well defined quantum gates (without significant decoherence) must be within the range of γ4×10-4 for not thermalized case, which was determined by using the purity parameter calculated at the end of the algorithm. For the thermalized case the decoherence is stablished for very small dissipation parameter, making almost not possible to implement this algorithm for not zero temperature.

Share and Cite:

G. López and P. López, "Study of Decoherence on the Teleportation Algorithm in a Chain of Three Nuclear Spins System," Journal of Modern Physics, Vol. 4 No. 1, 2013, pp. 68-75. doi: 10.4236/jmp.2013.41012.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] G. Lopez, M. Murgua and M. Sosa, “Quantization of One-Dimensional Free Particle Motion with Dissipation,” Modern Physics Letters B, Vol. 15, No. 22, 2001, p. 965. doi:10.1142/S0217984901002750
[2] A. O. Caldeira and A. T. Legget, “Path Integral Approach to Quantum Brownian Motion,” Physica A, Vol. 121, No. 3, 1983, pp. 587-616. doi:10.1016/0378-4371(83)90013-4
[3] W. G. Unruh and W. H. Zurek, “Reduction of a Wave Packet in Quantum Brownian Motion,” Physical Review D, Vol. 40, No. 4, 1989, pp. 1071-1094. doi:10.1103/PhysRevD.40.1071
[4] A. Venugopalan, “Decoherence and Schodinger-Cat States in a Stern-Gerlach-Type Experiment,” Physical Review A, Vol. 56, No. 5, 1997, pp. 4307-4310. doi:10.1103/PhysRevA.56.4307
[5] H. D. Zeh, “Toward Quantum Theory of Observation,” Foundations of Physics, Vol. 3, No. 1, 1973, pp. 109-116. doi:10.1007/BF00708603
[6] J. P. Paz and W. H. Zurek, “Environment-Induced Decoherence, Classicality and Consistency of Quantum Histories and the Transition from Quantum to Classical,” Physical Review D, Vol. 48, No. 6, 1993, pp. 2728-2738. doi:10.1103/PhysRevD.48.2728
[7] G. Lindblad, “On the Generators of Quantum Dynamical Semigroups,” Communications in Mathematical Physics, Vol. 48, No. 2, 1976, pp. 119-130. doi:10.1007/BF01608499
[8] A. J. Legget, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. Zwerger, “Dynamics of the Dissipative Two-State System,” Reviews of Modern Physics, Vol. 59, No. 1, 1987, pp. 1-85. doi:10.1103/RevModPhys.59.1
[9] W. H. Zurek, “Decoherence, Einselection, and the Quantum Origins of the Classical,” Reviews of Modern Physics, Vol. 75, No. 3, 2003, pp. 715-775. doi:10.1103/RevModPhys.75.715
[10] M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” Cambridge University Press, Cambridge, 2000.
[11] H.-P. Breuer and F. Petruccione, “The Theory of Open Quantum Systems,” Oxford University Press, Oxford, 2006.
[12] C. H. Benneth, G. Brassard, C. Crepeau, R. Jozsa, A. Peres and W. K. Wootters, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,” Physical Review Letters, Vol. 70, No. 13, 1993, pp. 1895-1899. doi:10.1103/PhysRevLett.70.1895
[13] M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri and J. Wineland, “Deterministic Quantum Teleportation of Atomic Qubits,” Nature, Vol. 429, 2004, pp. 737- 739. doi:10.1038/nature02608
[14] G. P. Berman, D. D. Doolen, D. I. Kamenev, G. V. Lopez and V. I. Tsifrinovich, “Perturbation Theory and Numerical Modeling of Quantum Logic Operations with Large Number of Qubits,” Contemporary Mathematics, Vol. 305, 2000, p. 13. doi:10.1090/conm/305/05213
[15] S. Das and G. S. Agarwal, “Decoherence Effects in Interacting Qubits under the Influence of Various Environments,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 42, No. 20, 2009, Article ID: 205502. doi:10.1088/0953-4075/42/20/205502
[16] N. P. Oxtopy, A. Rivas, S. F. Huelga and R. Fazio, “Probing a Composite Spin-Boson Environment,” New Journal of Physics, Vol. 11, 2009, Article ID: 063028. doi:10.1088/1367-2630/11/6/063028
[17] A. Shabani and D. A. Lindar, “Completely Positive Post-Markovian Master Equation via a Measurement Approach,” Physical Review A, Vol. 71, No. 2, 2005, Article ID: 020101R. doi:10.1103/PhysRevA.71.020101
[18] I. de Vega, D. Alonso and P. Gaspard, “Two-Level System Immersed in a Photonic Band-Gap Material: A Non-Markovian Stochastic Schr?dinger-Equation Approach,” Physical Review A, Vol. 71, No. 2, 2005, Article ID: 023812. doi:10.1103/PhysRevA.71.023812
[19] G. V. Lopez and L. Lara, “Numerical Simulation of a Controlled-Controlled-Not (CCN) Quantum Gate in a Chain of Three Interacting Nuclear Spins System,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 39, No. 18, 2006, p. 3897. doi:10.1088/0953-4075/39/18/019
[20] G. V. Lopez, J. Quezada, G. P. Berman, D. D. Doolen and V. I. Tsifrinovich, “Numerical Simulation of a Quantum Controlled-Not Gate Implemented on Four-Spin Molecules at Room Temperature,” Journal of Optics B: Quantum and Semiclassical Optics, Vol. 5, No. 2, 2003, p. 184. doi:10.1088/1464-4266/5/2/311
[21] G. V. Lopez, T. Gorin and L. Lara, “Simulation of Grover’s Quantum Search Algorithm in an Ising-Nuclear-Spin-Chain Quantum Computer with First-And-Second-Nearest-Neighbor Couplings,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 41, No. 5, 2008, Article ID: 055504. doi:10.1088/0953-4075/41/5/055504
[22] N. Y. Yao, L. Jiang, A. V. Gorshkov, P. C. Maurer, G. Giedke, J. I. Cirac and M. D. Lukin, “Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor,” arXiv:1012.2864v1, 2002.
[23] S. Lloyd, “A Potential Realizable Quantum Computer,” Science, Vol. 261, No. 5128, 1993, pp. 1569-1571. doi:10.1126/science.261.5128.1569
[24] P. Lopez and G. V. Lopez, “Quasi Non-Markovian Approach to the Study of Decoherence of a Controlled-Not Quantum Gate in a Chain of Few Nuclear Spins Quantum Computer,” Journal of Modern Physics, Vol. 3, No. 9, 2012, pp. 902-917. doi:10.4236/jmp.2012.31013
[25] G. V. Lopez and P. Lopez, “Study of Decoherence of Elementary Gates Implemented in a Chain of Few Nuclear Spins Quantum Computer Model,” Journal of Modern Physics, Vol. 3, No. 1, 2012, pp. 85-101. doi:10.4236/jmp.2012.39118

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.