Entanglement and Absorbing-State Transitions in Interactive Quantum Dynamics

TL;DR

This paper investigates how measurement and feedback in quantum systems can induce phase transitions, including entanglement and absorbing-state transitions, and how these are affected by the target state and system dynamics.

Contribution

It introduces a framework for analyzing measurement-based steering in quantum many-body systems and distinguishes between entanglement and absorbing-state transitions with their critical properties.

Findings

Absorbing-state transition occurs at different parameters than entanglement transition.

Steering effectiveness depends on the target state's nature, especially for long-range correlated states.

Entanglement and steering transitions are separated in parameter space for certain dynamics.

Abstract

Nascent quantum computers motivate the exploration of quantum many-body systems in nontraditional scenarios. For example, it has become natural to explore the dynamics of systems evolving under both unitary evolution and measurement. Such systems can undergo dynamical phase transitions in the entanglement properties of quantum trajectories conditional on the measurement outcomes. Here, we explore dynamics in which one attempts to (locally) use those measurement outcomes to steer the system toward a target state, and we study the resulting phase diagram as a function of the measurement and feedback rates. Steering succeeds when the measurement and feedback rates exceed a threshold, yielding an absorbing-state transition in the trajectory-averaged density matrix. We argue that the absorbing-state transition generally occurs at different critical parameters from the entanglement transition in individual trajectories and has distinct critical properties. The efficacy of steering depends on the nature of the target state: in particular, for local dynamics targeting long-range correlated states, steering is necessarily slow and the entanglement and steering transitions are well separated in parameter space.