Quantum synchronization in XX chains under relaxation

arXiv:2611.14657v1 Announce Type: new Abstract: We study stable synchronization in qubit XX chains with site-dependent frequencies and exchange couplings under multi-local amplitude damping noise, extending the uniform-chain results of B. \c{C}akmak et al., [Phys. Rev. A 114, L030202 2026] in several directions. We establish that the dark-mode energies are precisely the eigenvalues shared by all undamped segments separated by the damped sites. Generic stable synchronization of the edge qubits occurs if and only if these segments share exactly one eigenvalue and this eigenvalue is nonzero, in which case every qubit on the support of the corresponding dark mode is synchronized with locking constants independent of the initial preparation.