Measurement-induced phase transition in space
arXiv:2607.12386
The paper studies how a deterministic spatial gradient of measurement probabilities in a monitored Clifford quantum circuit creates coexisting volume‑law, critical, and area‑law entanglement regions, allowing the measurement‑induced phase transition to be probed via spatial scaling without temporal driving.
Abstract
Measurement-induced phase transitions (MIPTs) in monitored quantum circuits are usually characterized by preparing steady states at different uniform measurement probabilities. Here we introduce a spatial realization of the MIPT by imposing a deterministic measurement gradient in a single monitored Clifford chain. The resulting steady state contains coexisting volume-law, critical, and area-law regions, with the point acting as a spatial critical cut. By scanning entanglement observables across this profile, we show that the transition is organized by a spatial scaling form. Although this structure is analogous to finite-time scaling in temporally driven MIPT, the spatial protocol has no Kibble-Zurek dynamics. Instead, the physical bounds impose a finite linear window, producing cutoff-controlled asymptotic regimes whose fitted exponents provide direct access to the correlation-length exponent . Our results establish spatially inhomogeneous measurements as a controlled route to engineer and probe measurement-induced criticality within a single steady state.
14 pages, 7 figures