  We introduce a general scheme to detect various multiparticle entanglement
structures from global non-permutationally invariant observables. In
particular, we derive bounds on the variance of non-permutationally invariant
and collective operators for the verification of $k$-party entanglement. For a
family of observables related to the spin structure factor, we give
quantitative bounds on entanglement that are independent of the total number of
particles. We introduce highly non-symmetric states with genuine multipartite
entanglement that is verifiable with the presented technique and discuss how
they can be prepared with trapped ions exploiting the high degree of control in
these systems. As a special case, our framework provides an alternative
approach to obtain a tight relaxation of the entanglement criterion by S{\o}
rensen and M{\o} lmer [Phys. Rev. Lett. 86, 4431 (2001)] that is free from
technical assumptions and allows to calculate the bounds with an improved
scaling in the detectable depth.

Quantum Physics