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Perturbation bounds for quantum Markov processes and their fixed points
1. R. Bhatia, Matrix Analysis (Springer, 1996).
3. S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. Büchler, and P. Zoller, “Quantum states and phases in driven open quantum systems with cold atoms,” Nat. Phys. 4, 878–883 (2008).
4. M. Kastoryano
and K. Temme
, “Quantum logarithmic Sobolev inequalities and rapid mixing
,” preprint arXiv:1207.3261
10. D. Reeb, M. J. Kastoryano, and M. M. Wolf, “Hilbert's projective metric in quantum information theory,” J. Math. Phys. 52(8), 082201 (2011).
14. E. Seneta, “Perturbation of the stationary distribution measured by ergodicity coefficients,” Adv. Appl. Probab. 20, 228–230 (1988).
15. O. Szehr
, D. Reeb
, and M. Wolf
, “Spectral convergence bounds for classical and quantum Markov processes
,” preprint arXiv:1301.4827
16. K. Temme, M. J. Kastoryano, M. B. Ruskai, M. M. Wolf, and F. Verstraete, “The chi[sup 2]-divergence and mixing times of quantum Markov processes,” J. Math. Phys. 51(12), 122201 (2010).
18. F. Versraete, M. Wolf, and I. Cirac, “Quantum computation and quantum-state engineering driven by dissipation,” Nat. Phys. 5(9), 633–636 (2009).
19. M. Wolf
and D. Perez-Garcia
, “The inverse eigenvalue problem for quantum channels
,” preprint arXiv:1005.4545
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We investigate the stability of quantum Markov processes with respect to perturbations of their transition maps. In the first part, we introduce a condition number that measures the sensitivity of fixed points of a quantum channel to perturbations. We establish upper and lower bounds on this condition number in terms of subdominant eigenvalues of the transition map. In the second part, we consider quantum Markov processes that converge to a unique stationary state and we analyze the stability of the evolution at finite times. In this way we obtain a linear relation between the mixing time of a quantum Markov process and the sensitivity of its fixed point with respect to perturbations of the transition map.
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