  We uncover a local order parameter for measurement-induced phase transitions:
the average entropy of a single reference qubit initially entangled with the
system. Using this order parameter, we identify scalable probes of
measurement-induced criticality (MIC) that are immediately applicable to
advanced quantum computing platforms. We test our proposal on a 1+1 dimensional
stabilizer circuit model that can be classically simulated in polynomial time.
We introduce the concept of a "decoding light cone" to establish the local and
efficiently measurable nature of this probe. We also estimate bulk and surface
critical exponents for the transition. Developing scalable probes of MIC in
more general models may be a useful application of noisy-intermediate scale
quantum (NISQ) devices, as well as point to more efficient realizations of
fault-tolerant quantum computation.
