A Single Conformal Coordinate Decodes Outcome-Resolved Measurement-Induced Entanglement
Abstract
A local measurement of a critical many-body state produces exponentially many microscopic outcomes, each defining a different conditioned quantum state. We ask how much information from one such outcome is actually needed to predict the entanglement that remains between two unmeasured regions. We show that, in critical quantum chains, the universal outcome-resolved Rényi entropy is asymptotically determined by a single compact conformal coordinate extracted directly from the measurement record. Compact-boson theory explains this compression: the universal entropy is insensitive to all spatially varying components of the boundary profile, retaining only a single relative compact zero mode. At the free-fermion XX point, exact lattice identities expose the microscopic structure underlying the decoder, while large-scale outcome-by-outcome calculations confirm its scaling prediction across different subsystem geometries and Rényi indices. Numerical calculations in interacting XXZ chains further show that the same microscopic coordinate continues to decode the conditional entropy without interaction-dependent retuning. Thus an exponentially large space of measurement outcomes is reduced, for this universal observable, to a single conformal degree of freedom, revealing an emergent Luttinger-liquid mechanism for outcome-resolved postmeasurement entanglement.
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BibTeX
@misc{khasseh2026single,
title = {{A Single Conformal Coordinate Decodes Outcome-Resolved Measurement-Induced Entanglement}},
author = {Reyhaneh Khasseh and M. A. Rajabpour},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07995},
eprint = {2610.07995},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07995},
}
RIS
TY - UNPB
TI - A Single Conformal Coordinate Decodes Outcome-Resolved Measurement-Induced Entanglement
AU - Reyhaneh Khasseh
AU - M. A. Rajabpour
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07995
UR - https://arxiv.org/abs/2610.07995
AB - A local measurement of a critical many-body state produces exponentially many microscopic outcomes, each defining a different conditioned quantum state. We ask how much information from one such outcome is actually needed to predict the entanglement that remains between two unmeasured regions. We show that, in critical quantum chains, the universal outcome-resolved Rényi entropy is asymptotically determined by a single compact conformal coordinate extracted directly from the measurement record. Compact-boson theory explains this compression: the universal entropy is insensitive to all spatially varying components of the boundary profile, retaining only a single relative compact zero mode. At the free-fermion XX point, exact lattice identities expose the microscopic structure underlying the decoder, while large-scale outcome-by-outcome calculations confirm its scaling prediction across different subsystem geometries and Rényi indices. Numerical calculations in interacting XXZ chains further show that the same microscopic coordinate continues to decode the conditional entropy without interaction-dependent retuning. Thus an exponentially large space of measurement outcomes is reduced, for this universal observable, to a single conformal degree of freedom, revealing an emergent Luttinger-liquid mechanism for outcome-resolved postmeasurement entanglement.
ER -