Sequential mixing condition for continuous-time entangled Markov chains

Abdessatar Souissi; Abdessatar Barhoumi; Abdessatar Souissi; Abdessatar Barhoumi

doi:10.3934/math.2026068

AIMS Mathematics

2026, Volume 11, Issue 1: 1637-1652. doi: 10.3934/math.2026068

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Sequential mixing condition for continuous-time entangled Markov chains

Abdessatar Souissi ^{1
,
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Abdessatar Barhoumi ^{2
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1.
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
2.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa P.O.Box: 400, 31982, Saudi Arabia

Received: 18 July 2025 Revised: 24 December 2025 Accepted: 09 January 2026 Published: 19 January 2026
MSC : 46L06, 47A35, 60J27, 82B31, 82C31

We established a continuous-time framework for entangled quantum Markov chains derived from classical continuous-time Markov processes. Unlike previous studies focused on discrete-time dynamics, we demonstrated that a robust mixing property emerges directly from the structural architecture of the underlying continuous-time process. Our analysis showed that inhomogeneous entangled chains exhibited path-independent convergence to a limiting distribution determined by asymptotic temporal parameters. The results motivated future study of these entangled Markov chains in connection with open quantum system dynamics and quantum master equations.
- entanglement,
- continuous-time,
- Markov chains,
- mixing,
- quantum theory,
- inhomogeneous
Citation: Abdessatar Souissi, Abdessatar Barhoumi. Sequential mixing condition for continuous-time entangled Markov chains[J]. AIMS Mathematics, 2026, 11(1): 1637-1652. doi: 10.3934/math.2026068

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Abstract

We established a continuous-time framework for entangled quantum Markov chains derived from classical continuous-time Markov processes. Unlike previous studies focused on discrete-time dynamics, we demonstrated that a robust mixing property emerges directly from the structural architecture of the underlying continuous-time process. Our analysis showed that inhomogeneous entangled chains exhibited path-independent convergence to a limiting distribution determined by asymptotic temporal parameters. The results motivated future study of these entangled Markov chains in connection with open quantum system dynamics and quantum master equations.

References

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