Synchronization in a dissipative quantum many-body system

Abstract:We study synchronization in the XX qubit chain subject to local or multi-local amplitude-damping noise. Analyzing the decoherence-free subspace (DFS) structure of the model, we show that it is completely determined by a simple number-theoretic function involving the noise sites and the chain length. We derive a closed-form expression for local qubit observables restricted to the DFS and prove that stable synchronization of the edge qubits for arbitrary initial states occurs \textit{if and only if} the DFS supports exactly one single-excitation eigenstate. We further show that this same condition also guarantees constant asymptotic entanglement between the edge qubits, so that generic stable synchronization and constant asymptotic entanglement necessarily coexist. By contrast, when the DFS supports multiple single-excitation eigenstates, synchronization becomes initial state dependent and may be entirely absent, even though stable oscillatory entanglement can persist indefinitely.

Main: 5 pages + 2 figures, Sup. Mat.: 5 pages

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2604.18707 [quant-ph]

(or arXiv:2604.18707v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.18707 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. A 114, L030202 (2026)

https://doi.org/10.1103/yrfl-y3z8 Focus to learn more DOI(s) linking to related resources

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