Usefulness of entanglement-assisted quantum metrology

Entanglement-assisted quantum communication employs preshared entanglement between sender and receiver as a resource. We apply the same framework to quantum metrology, introducing shared entanglement between the probe and the ancilla in the preparation stage and allowing entangling operations at the measurement stage, i.e., using some entangled ancillary system that does not interact with the system to be sampled. This is known to be useless in the noiseless case, but was recently shown to be useful in the presence of noise [R. Demkowicz-Dobrzanski and L. Maccone, Phys. Rev. Lett. 113, 250801 (2014); W. Dur, M. Skotiniotis, F. Frowis, and B. Kraus, ibid. 112, 080801 (2014); E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, ibid. 112, 150802 (2014); R. Demkowicz-Dobrzanski and J. Kolodynski, New J. Phys. 15, 073043 (2013)]. Here we detail how and when it can be of use. For example, surprisingly it is useful when two channels are randomly alternated, for both of which ancillas do not help (depolarizing). We show that it is useful for all levels of noise for many noise models and propose a simple optical experiment to test these results.