QI
In the literature: open
Universality of the charge-sharpening transition in U(1) monitored circuits
In plain words
When circuits conserve a quantity like total charge, a second transition appears: below it, an observer cannot quickly learn the total charge from the measurements. Which universal class this learning transition belongs to is not settled.
Precise statement
In $1+1\mathrm{D}$ monitored circuits conserving $U(1)$ charge, a charge-sharpening transition at $p_{\#} < p_{c}$ separates phases where the total charge can or cannot be inferred from the measurement record in time $\operatorname{O}(L)$. Determine its universality class; a Kosterlitz-Thouless-type field theory was proposed (Barratt et al. 2022).
What would settle it
Large-scale numerics of finite-q circuits matched to field-theory predictions for the scaling of charge variance and learning time.