Bridge 3: measurements and the zero-cost obstruction

The classical-percolation toy reduction for measured circuits is not the positive exponential model SkinnerRuhmanNahum. The following monitored version of Section sec:bridge2 makes the obstruction exact.

Independently for every edge, choose $m_e\sim \mathrm{Bernoulli}(p)$. If $m_e=1$, measure one endpoint mode in the number basis and retain the complete outcome. If $m_e=0$, do not measure the pair.