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On a ψ-Mixing property for Entangled Markov Chains

Author

Listed:
  • Souissi, Abdessatar
  • Soueidy, El Gheteb
  • Barhoumi, Abdessatar

Abstract

We study a mixing condition for entangled Markov chains, so-called ψ-mixing property. We prove that every entangled Markov chain, whose Markov operators satisfy the Markov–Dobrushin condition, is ψ-mixing. Moreover, we show the restriction of the underlying QMC to the diagonal algebra gives rise to a classical mixing Markov chains with the same exponential rate of convergence.

Suggested Citation

  • Souissi, Abdessatar & Soueidy, El Gheteb & Barhoumi, Abdessatar, 2023. "On a ψ-Mixing property for Entangled Markov Chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).
    • Handle: RePEc:eee:phsmap:v:613:y:2023:i:c:s0378437123000882
    DOI: 10.1016/j.physa.2023.128533
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    References listed on IDEAS

    as
    1. Aldous, David & Lovász, László & Winkler, Peter, 1997. "Mixing times for uniformly ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 165-185, November.
    2. Bradley, Richard C., 1997. "Every "lower psi-mixing" Markov chain is "interlaced rho-mixing"," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 221-239, December.
    3. Barhoumi, Abdessatar & Souissi, Abdessatar, 2022. "Recurrence of a class of quantum Markov chains on trees," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    Full references (including those not matched with items on IDEAS)

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