IJPAM: Volume 109, No. 4 (2016)
DECOHERENCE-FREE SUBSPACES FOR
OPEN QUANTUM RANDOM WALKS ON GRAPHS
OPEN QUANTUM RANDOM WALKS ON GRAPHS
J. Agredo
Department of Mathematics
National University of Colombia
Department of Mathematics
Colombian School of Engineering Julio Garavito
Bogotá, COLOMBIA
Department of Mathematics
National University of Colombia
Department of Mathematics
Colombian School of Engineering Julio Garavito
Bogotá, COLOMBIA
Abstract. We study decoherence-free subspaces in a type of Quantum Markov Semigroups called continuous-time open quantum random walks on graphs. We measure the temporary changes of quantum correlations using geometric quantum discord with bures distance under some assumptions about the semigroup. In particular, we characterize the decay of correlations to zero, showing that turns out to be closely related with the structure of decoherence-free subspace.
Received: May 31, 2016
Revised: August 29, 2016
Published: October 9, 2016
AMS Subject Classification: 47D06, 46L55, 81S22
Key Words and Phrases: quantum Markov semigroup, geometric quantum discord, Bures distance, decoherence-free subspaces
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Bibliography
- 1
- J. Agredo, F. Fagnola and R. Rebolledo, Decoherence-free subspaces of a quantum Markov semigroup, J. Math. Phys, 55, (2014),11-32.
- 2
- A. Barchielli and C. Pellegrini, Jump-difusion unravelling of a non-Markovian generalized Lindblad master equation, J. Math. Phys, 51, (2010), 112104.
- 3
- Ph. Blanchard, and R. Olkiewicz, Decoherence induced transition from quantum to classical dynamics, Rev. Math. Phys, 15, (2003), 217-243 .
- 4
- Ph. Blanchard, and R. Olkiewicz, Decoherence as irreversible dynamical process in open quantum systems, Open quantum systems. III, Lectures Notes in Math., 1882, Springer, Berlin, (2006).
- 5
- R. Carbone, E. Sasso, and V. Umanità, Decoherence for Quantum Markov Semigroups on Matrix Algebras, Annales Henri Poincaré, 14, (2013), 17-37.
- 6
- L. Chaobin and B. Radhakrishnan, Continuous-time open quantum walks, arXiv:quant-ph/1604.05652v1,(2016)
- 7
- L. Chuang and M. Nielsen Quantum Computation and Quantum Information , Cambridge University Press, Cambridge (2000).
- 8
- I.L. Chuang, D.A. Lidar and K.B. Whaley, Decoherence-free Subspaces for Quantum Computation, Phys. Rev. Lett, 81, (1998), 2594.
- 9
- K. Conrad, Tensor product II, expository paper, https://www.math.uconn.edu/ kconrad/blurbs/
- 10
- J. Deschamps and V. Umanità, The decoherence-free subalgebra for continuous-time open quantum random walks, preprint, (2014).
- 11
- A. Dhahri, F. Fagnola and R. Rebolledo, The decoherence-free subalgebra of a quantum Markov semigroup with unbounded generator, Infin. Dimens. Anal. Quantum Probab. Relat, Top., 13, (2010), 413-433.
- 12
- F. Fagnola, Quantum Markov Semigroups and Quantum Markov Flows, Proyecciones, 18, (1999), 1-144.
- 13
- F. Fagnola and R. Rebolledo, Algebraic conditions for convergence of a quantum Markov semigroup to a steady state, Infin. Dimens. Anal. Quantum Probab. Relat. Top, 11, (2008), 467-474.
- 14
- D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I. Stamatescu and H. D. Zeh, Decoherence and the appearance of a classical world in quantum theory, Springer, (1996).
- 15
- D. Lidar, Review of Decoherence Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling, Adv. Chem. Phys. 154, (2014), 295-354.
- 16
- M. Orszag and D. Spehner, Geometric quantum discord with Bures distance, New. Jour. Phys, 15, (2013), 103001.
- 17
- M. Orszag and D. Spehner, Geometric quantum discord with Bures distance: the qubit case,J. Phys. A: Math. Theor, 47, (2014), 035302.
- 18
- K.R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Monographs in Mathematics, Vol. 85, (1992).
- 19
- C. Pellegrini, Continuous-Time Open Quantum Random Walks and Non-Markovian Lindblad Master Equations, J. Stat. Phys, 154, 3 (2014), 838-865.
- 20
- R. Rebolledo, Decoherence of quantum Markov semigroups, Ann. Inst. Henri Poincaré (B) Probab. Stat, 41, (2005), 349-373.
- 21
- R. Rebolledo, A view on decoherence via master equations, Open Sys. Inf. Dyn, 12, (2005), 37-54.
- 22
- W. Roga, D. Spehner and F. Illuminti, Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations, J. Phys. A: Math. Theor, 49,(2016), 235301.
- 23
- D. Spehner, Quantum correlations and distinguishability of quantum states, J. Math. Phys,55,(2014), 075211.
- 24
- F. Ticozzi and L. Viola, Quantum Markovian Subsystems: Invariance, Attractivity, and Control, IEEE Trans. Automat Control 53, (2008), 2048.
- 25
- W.H. Zurek, Decoherence and the Transition from Quantum to Classical, Physics Today, 44, (1991), 36-44.
.
DOI: 10.12732/ijpam.v109i4.16 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 4
Pages: 941 - 957
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