Universality of the cross-entropy in Z2 symmetric monitored quantum circuits

In monitored quantum many-body dynamics, information about the evolving state can ``leak'' into the measurement record, as quantified by the linear-cross entropy (LXE). Here, the authors show that the LXE serves as an order parameter that also distinguishes various area-law-entangled phases of monitored circuits with a global Ising symmetry. The behavior of the LXE at a critical point separating these phases quantitatively agrees with predictions from the conformal field theory describing this critical point. This connection between out-of-equilibrium dynamics and equilibrium statistical mechanics suggests the possibility of the LXE as a probe of universal critical behavior in other kinds of monitored quantum evolution.