Resolution-enhanced entanglement detection

We formulate a general family of entanglement criteria for multipartite states on arbitrary Hilbert spaces. Fisher information criteria compare the sensitivity to unitary rotations with the variances of suitable local observables. Generalized squeezing-type criteria provide lower bounds that are less stringent but require only measurements of second moments. The enhancement due to local access to the individual subsystems is studied in detail for the case of N spin-1/2 particles. The discussed techniques can be readily implemented in current experiments with trapped ions in Paul traps and neutral atoms in optical lattices.