  We experimentally demonstrate a general criterion to identify entangled
states useful for the estimation of an unknown phase shift with a sensitivity
higher than the shot-noise limit. We show how to exploit this entanglement on
the examples of a maximum likelihood as well as of a Bayesian phase estimation
protocol. Using an entangled four-photon state we achieve a phase sensitivity
clearly beyond the shot-noise limit. Our detailed comparison of methods and
quantum states for entanglement enhanced metrology reveals the connection
between multiparticle entanglement and sub-shot-noise uncertainty, both in a
frequentist and in a Bayesian phase estimation setting.
