  Dicke states represent a class of multipartite entangled states that can be
generated experimentally with many applications in quantum information. We
propose a method to experimentally detect genuine multipartite entanglement in
the vicinity of arbitrary Dicke states. The detection scheme can be used to
experimentally quantity the entanglement depth of many-body systems and is easy
to implement as it requires to measure only three collective spin operators.
The detection criterion is strong as it heralds multipartite entanglement even
in cases where the state fidelity goes down exponentially with the number of
qubits.
