Using adaptiveness and causal superpositions against noise in quantum metrology

We derive new bounds on achievable precision in the most general adaptive quantum metrological scenarios. The bounds are proven to be asymptotically saturable and equivalent to the known parallel scheme bounds in the limit of large number of channel uses. This completely solves a long standing conjecture in the field of quantum metrology on asymptotic equivalence between parallel and adaptive strategies. The new bounds also allow to easily assess the potential benefits of invoking the non-standard causal superposition strategies, for which we prove, similarly to the adaptive case, the lack of asymptotic advantage over the parallel ones.Comment: We added proof that the causal superposition channel from appendix C is well defined. We showed how to obtain a tighter bound for a parallel case (appendix D3