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Open quantum random walks formulated with quantum Bernoulli noises.

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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]
Copyright of International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 192347500
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  Data: Open quantum random walks formulated with quantum Bernoulli noises.
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  Data: <searchLink fieldCode="AR" term="%22Chen%2C+Jinshu%22">Chen, Jinshu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> emily-chen@126.com</i><br /><searchLink fieldCode="AR" term="%22Sun%2C+Jiahao%22">Sun, Jiahao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Fu%2C+Haoying%22">Fu, Haoying</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="DE" term="%22Graph+connectivity%22">Graph connectivity</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+operators%22">Quantum operators</searchLink><br /><searchLink fieldCode="DE" term="%22Ergodic+theory%22">Ergodic theory</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink>
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  Data: 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]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0217751X26500685
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        Text: English
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      – SubjectFull: Ergodic theory
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      – SubjectFull: Markov processes
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      – TitleFull: Open quantum random walks formulated with quantum Bernoulli noises.
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              Text: 3/30/2026
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              Y: 2026
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