Optimality of Lindblad unfolding in measurement phase transitions

TL;DR

This paper investigates measurement phase transitions in hybrid quantum circuits, demonstrating that measurement-averaged dynamics do not fully capture individual trajectory phases and that certain entanglement behaviors are unavoidable, impacting quantum simulation.

Contribution

It reveals that generalized measurements with identical averages can produce different phases, and shows that volume law entanglement phases are unavoidable in these models.

Findings

Measurement-averaged destruction of Bell states correlates with entanglement phases.

Different measurement schemes with the same average can lead to distinct phase transitions.

Volume law entanglement phase cannot be avoided in the studied models.

Abstract

Entanglement phase transitions in hybrid quantum circuits describe individual quantum trajectories rather than the measurement-averaged ensemble, despite the fact that results of measurements are not conventionally used for feedback. Here, we numerically demonstrate that a class of generalized measurements with identical measurement-averaged dynamics give different phases and phase transitions. We show that measurement-averaged destruction of Bell state entanglement is a useful proxy for determining which hybrid circuit yields the lowest-entanglement dynamics. We use this to argue that no unfolding of our model can avoid a volume law phase, which has implications for simulation of open quantum systems.