Bound state in the continuum and multiple atom state transfer applications in a waveguide QED setup

Bound states in the continuum (BICs) have been extensively exploited to enhance light--matter interactions in metamaterials, yet their emergence and utility in multi-atom waveguide platforms remain far less explored. Here we study atom--waveguide-dressed BICs in a one-dimensional coupled-resonator waveguide, where two spatially separated atomic arrays couple to distinct resonators with time-dependent strengths. We show that these BICs support a standing-wave photonic mode and enable the transfer of an arbitrary unknown quantum state between the two arrays with fidelities exceeding $99\%$. The protocol remains robust against both disorder and intrinsic dissipation. Our results establish BICs as long-lived resources for high-fidelity quantum information processing in waveguide-QED architectures.