  We show that multipartite quantum states that have a positive partial
transpose with respect to all bipartitions of the particles can outperform
separable states in linear interferometers. We introduce a powerful iterative
method to find such states. We present some examples for multipartite states
and examine the scaling of the precision with the particle number. Some
bipartite examples are also shown that possess an entanglement very robust to
noise. We also discuss the relation of metrological usefulness to Bell
inequality violation. We find that quantum states that do not violate any Bell
inequality can outperform separable states metrologically. We present such
states with a positive partial transpose, as well as with a non-positive
positive partial transpose.
