Spectral analysis for a multi-dimensional split-step quantum walk with a defect

This paper studies the spectrum of a multi-dimensional split-step quantum walk with defect that cannot be analyzed in previous papers by Fuda et al. (Quantum Inf Process 18:203–226, 2017; J Math Phys 59:082201, 2018). To this end, we have developed new technique which allow us to use spectral mapping theorem for one-defect model. We also derive time-averaged limit measure one-dimensional case as an application analysis.