One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909396840218624 |
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| author | De la Iglesia, Manuel D. Lardizabal, Carlos F. |
| author_facet | De la Iglesia, Manuel D. Lardizabal, Carlos F. |
| contents | Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal (quantum) degrees of freedom. In this work we study continuous-time QMCs on the integer line, half-line and finite segments, so that we are able to obtain exact probability calculations in terms of the associated matrix-valued orthogonal polynomials and measures. The methods employed here are applicable to a wide range of settings, but we will restrict to classes of examples for which the Lindblad generators are induced by a single positive map, and such that the Stieltjes transforms of the measures and their inverses can be calculated explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures De la Iglesia, Manuel D. Lardizabal, Carlos F. Quantum Physics Mathematical Physics Classical Analysis and ODEs 81S22, 42C05 Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal (quantum) degrees of freedom. In this work we study continuous-time QMCs on the integer line, half-line and finite segments, so that we are able to obtain exact probability calculations in terms of the associated matrix-valued orthogonal polynomials and measures. The methods employed here are applicable to a wide range of settings, but we will restrict to classes of examples for which the Lindblad generators are induced by a single positive map, and such that the Stieltjes transforms of the measures and their inverses can be calculated explicitly. |
| title | One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures |
| topic | Quantum Physics Mathematical Physics Classical Analysis and ODEs 81S22, 42C05 |
| url | https://arxiv.org/abs/2402.15878 |