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arXiv · 2602.23868

Non-commutative Index of Measurement-only Entanglement Phase Transition

Zhichen Huang·Chunxiao Du·Yang Zhou·Zhisong Xiao
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Abstract

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 for spatially and temporally homogeneous Pauli stabilizer measurement-only circuits. By applying this index to three representative measurement-only models, we find that 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 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.

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Zhichen Huang, Chunxiao Du, Yang Zhou, Zhisong Xiao. 2026-02-27. Non-commutative Index of Measurement-only Entanglement Phase Transition. https://doi.org/10.1103/lfjz-cm8k

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