  The mechanism by which an effective macroscopic description of quantum
measurement in terms of discrete, probabilistic collapse events emerges from
the reversible microscopic dynamics remains an enduring open question. Emerging
quantum computers offer a promising platform to explore how measurement
processes evolve across a range of system sizes while retaining coherence.
Here, we report the experimental observation of evidence for an
observable-sharpening measurement-induced phase transition in a chain of
trapped ions in Quantinuum H1-1 system model quantum processor. This transition
manifests as a sharp, concomitant change in both the quantum uncertainty of an
observable and the amount of information an observer can (in principle) learn
from the measurement record, upon increasing the strength of measurements. We
leverage insights from statistical mechanical models and machine learning to
design efficiently-computable algorithms to observe this transition (without
non-scalable post-selection on measurement outcomes) and to mitigate the
effects on errors in noisy hardware.
