Non-commutative Index of Measurement-only Entanglement Phase Transition
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917315050733568 |
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| author | Huang, Zhichen Du, Chunxiao Zhou, Yang Xiao, Zhisong |
| author_facet | Huang, Zhichen Du, Chunxiao Zhou, Yang Xiao, Zhisong |
| contents | Measurement-only models offer an ideal platform for exploring entanglement dynamics in the absence of unitary evolution. Despite extensive numerical evidence for entanglement phase transitions in measurement-only dynamics, the underlying mechanism attributed to non-commutativity among multi-site projective measurements has remained qualitative and coarse-grained. In this work, we identify a quantitative non-commutative index. By applying this index into three representative measurement-only models, we elucidate the role of non-commutativity in measurement-only dynamics: the emergence of a volume-law phase is governed by the non-commutative structure of the measurement ensemble, while the transition point is quantitatively determined by the amount of critical non-commutativity. More strikingly, the critical non-commutativity exhibits a universal linear scaling with the measurement range, independent of the microscopic details of the measurement ensembles. Our findings deepen the understanding of the fundamental mechanism behind the measurement-only entanglement phase transition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_23868 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-commutative Index of Measurement-only Entanglement Phase Transition Huang, Zhichen Du, Chunxiao Zhou, Yang Xiao, Zhisong Quantum Physics Measurement-only models offer an ideal platform for exploring entanglement dynamics in the absence of unitary evolution. Despite extensive numerical evidence for entanglement phase transitions in measurement-only dynamics, the underlying mechanism attributed to non-commutativity among multi-site projective measurements has remained qualitative and coarse-grained. In this work, we identify a quantitative non-commutative index. By applying this index into three representative measurement-only models, we elucidate the role of non-commutativity in measurement-only dynamics: the emergence of a volume-law phase is governed by the non-commutative structure of the measurement ensemble, while the transition point is quantitatively determined by the amount of critical non-commutativity. More strikingly, the critical non-commutativity exhibits a universal linear scaling with the measurement range, independent of the microscopic details of the measurement ensembles. Our findings deepen the understanding of the fundamental mechanism behind the measurement-only entanglement phase transition. |
| title | Non-commutative Index of Measurement-only Entanglement Phase Transition |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.23868 |