Universal Scaling and Conformal Symmetry in Measurement-Induced Entanglement Transitions — E8 Intelligence Research

FINDING: Measurement-induced entanglement phase transitions (MIPT) in monitored quantum systems reveal a sharp critical point separating volume-law (entangling) from area-law (disentangling) phases, with universal scaling governed by conformal field theory and effective central charge. | MATH: Critical point at measurement rate \( p_c \); entanglement entropy \( S \sim \frac{c}{6} \log L \) at criticality (1+1D), with \( c \) the effective central charge; scaling exponents \( \nu \) for correlation length \( \xi \sim |p-p_c|^{-\nu} \); for Haar random circuits, \( c \approx 0.26 \)–\( 0.34 \) depending on measurement basis; in fermionic systems, \( c \) can be computed exactly via free-fermion techniques; dynamic exponent \( z = 1 \) (conformal invariance). | CONNECTION: The critical point exhibits conformal symmetry — the same algebraic structure underlying the modular group \( \mathrm{PSL}(2,\mathbb{Z}) \) and elliptic curves. The effective central charge \( c \) relates to the Viras Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com