Universal phase correction for quantum state transfer in one-dimensional topological spin chains

Gap-protected topological channels are a promising way to realize robust and high-fidelity state transfer in quantum networks. Although various topological transfer protocols based on the Su-Schrieffer-Heeger model or its variants have been proposed, the phase accumulation during the evolution, as an essential aspect, is underestimated. Here, by numerically studying the phase information of quantum state transfer (QST) in one-dimensional (1D) topological spin chains, we uncover a universal phase correction $\phi_0 =(N-1)\pi/2$ for both adiabatic and diabatic topological schemes. Interestingly, the site-number-dependent phase correction satisfies $\mathbb{Z}_{4}$ symmetry and is equally effective for perfect mirror transmission in spin chains. Our work reveals a universal phase correction in 1D topologically protected QST, which will prompt a reevaluation of the topological protection mechanism in quantum systems.