Controlling Entanglement at Absorbing State Phase Transitions in Random Circuits

No prior work had resolved how active feedback mechanisms modify the universal behavior of quantum systems undergoing measurement-induced transitions. Prior research has shown that unitary dynamics combined with frequent observations lead to distinct phases of information spread. That uncertainty drove the investigation into how steering these systems toward stable configurations alters their entanglement properties. It was already known that random circuits exhibit complex phase structures under various measurement protocols. This gap motivated a detailed look at the interplay between control operations and state stability. Researchers have long sought to understand if these transitions share common features with classical absorbing state models. The current landscape of quantum information science lacks a comprehensive framework for linking these two phenomena. This study addresses the missing connection between feedback-driven stability and entanglement entropy scaling.

The aim of this study is to investigate the behavior of entanglement entropy at absorbing state phase transitions within random circuits subjected to feedback control. The researchers seek to understand how steering quantum dynamics toward stable states modifies the standard phenomenology of measurement-induced transitions. This investigation addresses the uncertainty regarding whether feedback-driven stability can be linked to the universal dynamics of classical absorbing state models. The authors examine the role of spatial range in control operations to determine its impact on phase structure. They explore the conditions under which entanglement entropy fluctuations couple to the order parameter of the absorbing state. The study also clarifies the distinction between these two types of transitions under various control protocols. By introducing a quantitative framework, the team provides a rigorous basis for evaluating these complex quantum phenomena. This work ultimately aims to improve the observability of phase transitions in monitored many-body systems.

Review Approach involves constructing a computational model using stabilizer circuits to simulate many-body quantum dynamics. The researchers integrate repeated measurements into these circuits to induce phase transitions. They implement feedback-control operations that actively steer the system toward a designated absorbing state. The team varies the spatial range of these control operations to observe different entanglement behaviors. They employ classical flag labels to track the state evolution within the stabilizer formalism. This approach allows for the quantitative calculation of entanglement entropy across various circuit configurations. The study compares short-range and long-range feedback protocols to identify distinct phase boundaries. This methodology provides a robust way to analyze the coupling between entropy fluctuations and absorbing state order parameters.

Key Findings From the Literature indicate that short-range control operations produce a transition between phases with unique subextensive scalings of entanglement entropy. In contrast, long-range feedback operations drive a transition between volume-law and area-law phases. The researchers observe that entanglement entropy fluctuations and the order parameter of the absorbing state transition become fully coupled under strongly entangling feedback. In these instances, the entanglement entropy adopts the universal dynamics of the absorbing state transition. The authors report that this coupling does not occur for arbitrary control operations. Consequently, the two transitions are generally distinct in most experimental configurations. The quantitative framework confirms that the spatial extent of the feedback is a critical factor in determining the phase structure. These results establish that feedback-driven dynamics significantly modify the standard phenomenology of measurement-induced transitions.

Synthesis and Implications suggest that feedback operations fundamentally alter the phase structure of quantum circuits. The authors demonstrate that short-range control leads to subextensive scaling differences between phases. Their analysis reveals that long-range operations induce a shift between volume-law and area-law entanglement regimes. The researchers propose that strong entangling feedback couples the fluctuations of entropy to the order parameter of the absorbing state. In this specific regime, the system adopts the universal dynamics characteristic of the absorbing state transition. The study clarifies that these two transitions remain distinct under arbitrary control conditions. These findings provide a new perspective on the observability of phase transitions in monitored quantum systems. The work highlights the sensitivity of quantum information dynamics to the spatial extent of feedback protocols.