Non-commutative Index of Measurement-only Entanglement Phase Transition

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.

12 pages, 13 figures

References in corpus (14)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Entanglement Transition in the Projective Transverse Field Ising Model
• Incompatible measurements in quantum information science
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Measurement-induced phase transition for free fermions above one dimension
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry
• Interplay among entanglement, measurement incompatibility, and nonlocality
• Measurement-induced phase transition in free bosons
• Probing prethermal nonergodicity through measurement outcomes of monitored quantum dynamics
• Measurement-Driven Transitions between Area Law Phases