This note provides a characterization of the subspaces of a complex Banach lattice which do stable phase retrieval, in the spirit of the characterization of real stable phase retrieval established by D. Freeman, T. Oikhberg, B. Pineau, and M. A. Taylor Math. Ann. 390 (2024), pp. 1–43.
Camúñez et al. (2026) studied this question.