Monitored long-range interacting systems: spin-wave theory for quantum trajectories

TL;DR

This paper introduces a spin-wave theory extension for analyzing monitored long-range interacting quantum systems, enabling efficient simulation of entanglement dynamics and phase transitions relevant to quantum technologies.

Contribution

We develop a systematic spin-wave approach at the quantum trajectory level for long-range interactions, broadening analysis capabilities beyond density matrix methods.

Findings

Entanglement transitions from logarithmic to volume law with changing interaction range.

The framework captures nonlinear dynamical features like entanglement and trajectory correlations.

Mitigates experimental post-selection challenges in detecting quantum phases.

Abstract

Measurement-induced phases exhibit unconventional dynamics as emergent collective phenomena, yet their behavior in tailored interacting systems -- crucial for quantum technologies -- remains less understood. We develop a systematic toolbox to analyze monitored dynamics in long-range interacting systems, relevant to platforms like trapped ions and Rydberg atoms. Our method extends spin-wave theory to general dynamical generators at the quantum trajectory level, enabling access to a broader class of states than approaches based on density matrices. This allows efficient simulation of large-scale interacting spins and captures nonlinear dynamical features such as entanglement and trajectory correlations. We showcase the versatility of our framework by exploring entanglement phase transitions in a monitored spin system with power-law interactions in one and two dimensions, where the entanglement scaling changes from logarithm to volume law as the interaction range shortens, and by dwelling on how our method mitigates experimental post-selection challenges in detecting monitored quantum phases.