arXiv:2509.10834v2 Announce Type: replace-cross Abstract: This paper studies the landscape of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Since the complicated sensing structure makes direct landscape analysis technically challenging, we introduce a tractable tensor sensing surrogate that preserves the essential low-rank structure. We first analyze its population risk, characterize the global landscape on the unit sphere, and establish local linear convergence of Riemannian gradient descent (RGD) under mild conditions. We then extend the analysis to tensor sensing under a tensor restricted isometry property (TRIP), establishing local geometric and RGD convergence guarantees, and quantify robustness to measurement noise. Our theoretical results are further supported by extensive numerical experiments. These findings offer insights into the optimization landscape of the surrogate tensor sensing problem, thereby providing guidance for studying and solving the original BDPR problem.