Measurement-induced multipartite-entanglement regimes in collective spin systems

Abstract

We study the competing effects of collective generalized measurements and interaction-induced scrambling in the dynamics of an ensemble of spin-1/2 particles at the level of quantum trajectories. This setup can be considered as analogous to the one leading to measurement-induced transitions in quantum circuits. We show that the interplay between collective unitary dynamics and measurements leads to three regimes of the average Quantum Fisher Information (QFI), which is a witness of multipartite entanglement, as a function of the monitoring strength. While both weak and strong measurements lead to extensive QFI density (i.e., individual quantum trajectories yield states displaying Heisenberg scaling), an intermediate regime of classical-like states emerges for all system sizes where the measurement effectively competes with the scrambling dynamics and precludes the development of quantum correlations, leading to sub-Heisenberg-limited states. We characterize these regimes and the crossovers between them using numerical and analytical tools, and discuss the connections between our findings, entanglement phases in monitored many-body systems, and the quantum-to-classical transition.

arXiv comment16 pages, 7 figures. Typos fixed, section IV. B added in v3 - v4 fixes minor formatting issues. Accepted for publication in Quantum

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• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Multipartite entanglement structure of monitored quantum circuits
• Dynamical multipartite entanglement in a generalized Tavis-Cummings model with XY spin interaction
• Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information
• Fractal structure of multipartite entanglement in monitored quantum circuits