A Markov–Dobrushin Inequality for Quantum Channels

Accardi, Luigi; Lu, Yun Gang; Souissi, Abdessatar

doi:10.1142/s1230161221500189

Open Syst. Inf. Dyn.

2021

DOI: 10.1142/s1230161221500189

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A Markov–Dobrushin Inequality for Quantum Channels

Luigi Accardi

Yun Gang Lu

Abdessatar Souissi

Abstract: We propose a quantum extension of the Markov-Dobrushin inequality. As an application, we estimate the Markov-Dobrushin constant for some classes of quantum Markov channels, in particular for the Pauli channel, widely studied in quantum information theory.

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Cited by 6 publications

References 15 publications

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Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains

Souissi,

Mukhamedov

2024

J Nonlinear Math Phys

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In the present paper, we introduce a class of F-stochastic operators on a finite-dimensional simplex, each of which is regular, ascertaining that the species distribution in the succeeding generation corresponds to the species distribution in the previous one in the long run. It is proposed a new scheme to define non-homogeneous Markov chains contingent on the F-stochastic operators and given initial data. By means of the uniform ergodicity of the non-homogeneous Markov chain, we define a non-homogeneous (quantum) entangled Markov chain. Furthermore, it is established that the non-homogeneous entangled Markov chain enables $$\psi$$ ψ -mixing property.

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Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains

Souissi,

Mukhamedov

2024

J Nonlinear Math Phys

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Recurrence of a class of quantum Markov chains on trees

Barhoumi¹,

Souissi²

2022

Chaos, Solitons & Fractals

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Entangled Hidden Markov Models

Souissi,

Soueidi

2023

Chaos, Solitons & Fractals

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A Markov–Dobrushin Inequality for Quantum Channels

Abstract: We propose a quantum extension of the Markov-Dobrushin inequality. As an application, we estimate the Markov-Dobrushin constant for some classes of quantum Markov channels, in particular for the Pauli channel, widely studied in quantum information theory.

Cited by 6 publications

References 15 publications

Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains

Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains

Recurrence of a class of quantum Markov chains on trees

Entangled Hidden Markov Models

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