Useful Multiparticle Entanglement and Sub-Shot-Noise Sensitivity in   Experimental Phase Estimation
  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. 
Roland Krischek, Christian Schwemmer, Witlef Wieczorek, Harald   Weinfurter, Philipp Hyllus, Luca Pezz\'e, and Augusto Smerzi
quant-ph