Multiparticle entanglement criteria for nonsymmetric collective variances

Understand

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.