Post-selected Criticality in Measurement-induced Phase Transitions

TL;DR

This paper explores how post-selection in measurement-induced phase transitions changes their universality class, revealing new critical exponents and linking them to entanglement transitions in random tensor networks.

Contribution

It demonstrates that explicit post-selection fundamentally alters the universality class of MIPT, with new critical exponents and a connection to RTN entanglement transitions.

Findings

Post-selection changes the universality class of MIPT.

Correlation-length exponent $ u oughly 2.1$ is larger than standard MIPT.

A minimum onsite dimension of 3 is needed for the transition.

Abstract

Information-theoretic phase transitions, such as the measurement-induced phase transition (MIPT), characterize the robustness of quantum dynamics to local monitoring and are naturally formulated in terms of trajectories conditioned on typical measurement outcomes, which are naively accessible only through post-selection. Here we implement forced measurements to investigate how explicit post-selection alters the nature of the transition. We find that post-selection fundamentally alters the universality class by reweighting trajectories that are otherwise rare. In particular, we obtain a correlation-length exponent $\nu\approx 2.1$ larger than that of the standard MIPT and a negative effective central charge $c_\mathrm{eff}\approx -0.4$. We also compare the post-selected MIPT to the entanglement transition of Random Tensor Networks (RTN), and demonstrate that their universality class is the same. This setup further allows time-periodic, translationally-invariant circuits with post-selected weak measurements. In both models, we find that an onsite dimension of at least 3 (qutrits but not qubits) is necessary to induce a transition.