Symmetry and Topology of Successive Quantum Feedback Control
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918510592000000 |
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| author | Wen, Junxuan Gong, Zongping Sagawa, Takahiro |
| author_facet | Wen, Junxuan Gong, Zongping Sagawa, Takahiro |
| contents | We establish a symmetry classification for a general class of quantum feedback control. For successive feedback control with a non-adaptive sequence of bare measurements (i.e., with positive Kraus operators), we prove that the symmetry classification collapses to the ten-fold AZ$^\dagger$ classes, specifying the allowed topology of CPTP maps associated with feedback control. We demonstrate that a chiral Maxwell's demon with Gaussian measurement errors exhibits quantized winding numbers. Moreover, for general (non-bare) measurements, we explicitly construct a protocol that falls outside the ten-fold classification. These results broaden and clarify the principles in engineering topological aspects of quantum control robust against disorder and imperfections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry and Topology of Successive Quantum Feedback Control Wen, Junxuan Gong, Zongping Sagawa, Takahiro Mesoscale and Nanoscale Physics Quantum Physics We establish a symmetry classification for a general class of quantum feedback control. For successive feedback control with a non-adaptive sequence of bare measurements (i.e., with positive Kraus operators), we prove that the symmetry classification collapses to the ten-fold AZ$^\dagger$ classes, specifying the allowed topology of CPTP maps associated with feedback control. We demonstrate that a chiral Maxwell's demon with Gaussian measurement errors exhibits quantized winding numbers. Moreover, for general (non-bare) measurements, we explicitly construct a protocol that falls outside the ten-fold classification. These results broaden and clarify the principles in engineering topological aspects of quantum control robust against disorder and imperfections. |
| title | Symmetry and Topology of Successive Quantum Feedback Control |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2509.12637 |