Hierarchy of tripartite entanglement detection in a cavity magnomechanical system

We propose a criterion for detecting quantum states containing non-zero entanglement with respect to all possible bipartitions of a tripartite system. Our criterion, together with two other criteria, forms a hierarchy of tripartite entanglement detection, revealing three distinct types: genuine tripartite entanglement, entanglement with respect to all bipartitions, and standard tripartite entanglement. Furthermore, we present a feasible scheme for generating and detecting this hierarchy of tripartite entanglement within a cavity magnomechanical system. Our research paves the way for generating and detecting tripartite entanglement hierarchies in continuous variable systems.