Detecting $k$-nonstretchability via a class of informationally complete symmetric measurements

Characterizing multipartite entanglement is a fundamental problem in quantum information theory. The concept of $k$-stretchability [Szalay, Quantum 3, 204 (2019)] provides a framework for describing multipartite entanglement structures. We investigate the detection of $k$-nonstretchability using informationally complete $(s,t)$-POVMs [Siudzi$\acute{\text{n}}$ska, Phys. Rev. A 105, 042209 (2022)], which encompass GSIC-POVMs and MUMs. Several criteria for $k$-nonstretchability in multipartite quantum systems are established. These criteria identify classes of $k$-nonstretchable states, and their applicability and advantages are demonstrated through explicit examples.