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Open quantum random walks formulated with quantum Bernoulli noises.

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Bibliographic Details
Title: Open quantum random walks formulated with quantum Bernoulli noises.
Authors: Chen, Jinshu1 (AUTHOR) emily-chen@126.com, Sun, Jiahao1 (AUTHOR), Fu, Haoying1 (AUTHOR)
Source: International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics. 3/30/2026, Vol. 41 Issue 9, p1-24. 24p.
Subjects: Graph connectivity, Quantum operators, Ergodic theory, Markov processes
Abstract: Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation (CAR) in equal time. This paper introduces a new type of fermionic open quantum random walk by formulating it with QBN on single-excitation subspaces. Within this framework, we establish a rigorous criterion for irreducibility, which requires the conjunction of strong graph connectivity, algebraic irreducibility of the transition operators and nonvanishing transition amplitudes. For finite irreducible walks, we prove convergence to a unique invariant state and establish strong convergence under the additional condition of aperiodicity. The theoretical framework is validated through a comprehensive two-node example, which illustrates both the convergence behavior and the intrinsic quantum features of the model. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation (CAR) in equal time. This paper introduces a new type of fermionic open quantum random walk by formulating it with QBN on single-excitation subspaces. Within this framework, we establish a rigorous criterion for irreducibility, which requires the conjunction of strong graph connectivity, algebraic irreducibility of the transition operators and nonvanishing transition amplitudes. For finite irreducible walks, we prove convergence to a unique invariant state and establish strong convergence under the additional condition of aperiodicity. The theoretical framework is validated through a comprehensive two-node example, which illustrates both the convergence behavior and the intrinsic quantum features of the model. [ABSTRACT FROM AUTHOR]
ISSN:0217751X
DOI:10.1142/S0217751X26500685