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

Abstract

Characterizing multipartite entanglement is a fundamental problem in quantum information theory. The concept of $k$-stretchability provides a framework for characterizing the structure of multipartite entanglement. We investigate $k$-nonstretchability using informationally complete $(s,t)$-positive operator-valued measures ($(s,t)$-POVMs) and derive two families of criteria. These criteria identify classes of $k$-nonstretchable states, and we demonstrate their applicability and advantages through explicit examples.