We apply the classical data processing inequality to quantum metrology to
show that manipulating the classical information from a quantum measurement
cannot aid in the estimation of parameters encoded in quantum states. We
further derive a quantum data processing inequality to show that coherent
manipulation of quantum data also cannot improve the precision in estimation.
In addition, we comment on the assumptions necessary to arrive at these
inequalities and how they might be avoided providing insights into enhancement
procedures which are not provably wrong.Comment: Comments encourage
