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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2501.01249 |
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| _version_ | 1866910060321439744 |
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| author | Loebens, Newton |
| author_facet | Loebens, Newton |
| contents | In this paper, we study the recurrence of Open Quantum Walks induced by finite-dimensional coins on the line ($\mathbb{Z}$) and on the grid ($\mathbb{Z}^2$). Two versions are considered: discrete-time open quantum walks (OQW) and continuous-time open quantum walks (CTOQW). We present three distinct recurrence criteria for OQWs on $\mathbb{Z}$, each adapted to different types of coins. The first criterion applies to coins whose auxiliary map has a unique invariant state, resulting in the first recurrence criterion for Lazy OQWs. The second one applies to Lazy OQWs of dimension 2, where we provide a complete characterization of the recurrence for this low-dimensional case. The third one presents a general criterion for finite-dimensional coins in the non-lazy case, which generalizes many of the previously known results for OQWs on $\mathbb{Z}$. Also, we present a general recurrence criterion for OQWs on $\mathbb{Z}^2$ via the open quantum jump chain, obtained from a recurrence criterion for CTOQWs on $\mathbb{Z}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01249 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recurrence Criteria for Reducible Homogeneous Open Quantum Walks on the Line Loebens, Newton Quantum Physics In this paper, we study the recurrence of Open Quantum Walks induced by finite-dimensional coins on the line ($\mathbb{Z}$) and on the grid ($\mathbb{Z}^2$). Two versions are considered: discrete-time open quantum walks (OQW) and continuous-time open quantum walks (CTOQW). We present three distinct recurrence criteria for OQWs on $\mathbb{Z}$, each adapted to different types of coins. The first criterion applies to coins whose auxiliary map has a unique invariant state, resulting in the first recurrence criterion for Lazy OQWs. The second one applies to Lazy OQWs of dimension 2, where we provide a complete characterization of the recurrence for this low-dimensional case. The third one presents a general criterion for finite-dimensional coins in the non-lazy case, which generalizes many of the previously known results for OQWs on $\mathbb{Z}$. Also, we present a general recurrence criterion for OQWs on $\mathbb{Z}^2$ via the open quantum jump chain, obtained from a recurrence criterion for CTOQWs on $\mathbb{Z}^2$. |
| title | Recurrence Criteria for Reducible Homogeneous Open Quantum Walks on the Line |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2501.01249 |