Infinitely fast critical dynamics: Teleportation through temporal rare regions in monitored quantum circuits

We consider measurement-induced phase transitions in monitored quantum circuits with a measurement rate that fluctuates in time, remaining spatially uniform at each time. The spatially correlated fluctuations in the measurement rate disrupt the volume-law phase for low measurement rates; at a critical measurement rate, they give rise to an entanglement phase transition with ``ultrafast’’ dynamics, i.e., spacetime ($x,t$) scaling $\log x \sim t^{ψ_τ}$. The ultrafast dynamics at the critical point can be viewed as a spacetime-rotated version of an infinite-randomness critical point; despite the spatial locality of the dynamics, ultrafast information propagation is possible because of measurement-induced quantum teleportation. We identify temporal Griffiths phases on either side of this critical point. We provide a physical interpretation of these phases, and support it with extensive numerical simulations of information propagation and entanglement dynamics in stabilizer circuits. The implications of our results on the general stability of phase transitions and ordered phases to such temporal randomness are discussed.

💡 Research Summary

The authors investigate measurement‑induced phase transitions (MIPTs) in one‑dimensional monitored quantum circuits where the measurement rate p(t) fluctuates uniformly in space but varies randomly in time. At each discrete time step the entire lattice is assigned the same measurement probability drawn from a uniform distribution, allowing the average rate (\bar p) to be tuned by a parameter n. In the limits n→0 (high constant p) the system is in an area‑law phase, while n→∞ (p≈0) yields a unitary volume‑law phase.

Temporal randomness creates “rare time intervals” in which p(t) is anomalously high or low. These intervals interrupt the growth of entanglement in the low‑p regime and, conversely, generate occasional long‑range entanglement in the high‑p regime. The authors identify temporal Griffiths phases on both sides of the transition, characterized by large fluctuations of entanglement entropy and mutual information that are of the same order as their mean values.

When the average measurement rate is tuned to a critical value (\bar p_c), the system undergoes a novel critical point that does not belong to the usual conformal field theory class (z = 1). Instead, the dynamical exponent vanishes, z → 0, leading to an “ultrafast” scaling law
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