All the research papers I found so far, are just showing measurement of the squeezing parameter or quantum Fisher Information (QFI). Of course authors mention that, due to large QFI or strong squeezing this setup can be used for metrological purposes beyond standard quantum limit (SQL). I could not find any papers, which actually perform estimation of the unknown phase and show that the precision is beyond SQL. I am curious from the point of view of estimation in the presence of decoherence (which is always present). Theoretical papers indicate that entangled states are basically useless if frequency is estimated (e.q. Ramsey spectroscopy).
I am not actually expert in this field and I am not sure whether the following paper is of your help, I just referred this if I could learn something from you and others.
Entanglement-free Heisenberg-limited phase estimation
BL Higgins, DW Berry, SD Bartlett, HM Wiseman, GJ Pryde, Nature 450 (7168), 393
Thank you @Mohammad Sayem Mahmood. The paper you referenced uses different technique for achieving sub-shot noise precision. Shortly speaking, the phase is imprinted multiple times on the single probe and does not require massive entanglement generation. Giovannetti et al. wrote about that in PRL 96, 010401 (2006).
In fact, there is no "quantum limit". This "taboo" is not inconclusive to violate, it must be "circumvented". Measure two "coordinates" not "at the same time", but at different, but close intervals of time. That's all.