Breakdown of Measurement-Induced Phase Transitions Under Information Loss

TL;DR

This paper investigates how partial information loss affects measurement-induced phase transitions in quantum systems, revealing that averaging over trajectories can obscure critical phase features and long-range correlations.

Contribution

It introduces an exactly-solvable Liouvillian model to analyze the impact of trajectory averaging on measurement-induced phase transitions.

Findings

Averaging over multiple trajectories introduces an effective finite lengthscale.

Partial averaging suppresses long-range correlations and blurs phase signatures.

Long-time spatial correlations are significantly affected by the degree of trajectory discrimination.

Abstract

The dynamics of a quantum-many body system subject to measurements is naturally described by an ensemble of quantum trajectories, which can feature measurement-induced phase transitions (MIPTs). This phenomenon cannot be revealed through ensemble-averaged observables, but it requires the ability to discriminate each trajectory separately, making its experimental observation extremely challenging. We explore the fate of MIPTs under an observer's reduced ability to discriminate each measurement outcome. This introduces uncertainty in the state of the system, causing observables to probe a restricted subset of trajectories rather than a single one. By introducing an exactly-solvable Liouvillian model, we examine how long-time spatial correlations are influenced by varying degrees of trajectory averaging. We compute exactly the correlation matrix, Liouvillian gap, and entanglement negativity to demonstrate that averaging over multiple realizations introduces an effective finite lengthscale, beyond which long-range correlations are suppressed. This suggests that partial averaging over trajectories conceals the critical features of individual realizations, thereby blurring away the signatures of distinct measurement-induced phases.