Synchronization in a dissipative quantum many-body system

We study synchronization in the XX qubit chain subject to local or multilocal amplitude-damping noise. We show that generic stable synchronization of the edge qubits occurs the decoherence-free subspace (DFS) supports exactly one single-excitation eigenstate. Analyzing the 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 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. Our analysis can be extended to any excitation-conserving qubit chain mappable to free fermions and is directly testable on platforms with site-selective dissipation.