Strategies for Estimating Quantum Lossy Channels

Due to the anisotropy of quantum lossy channels one must choose optimal bases of input states for best estimating them. In this paper, we obtain that the equal probability Schr\"{o}dinger cat states are optimal for estimating a single lossy channel and they are also the optimal bases of input states for estimating composite lossy channels. On the other hand, by using the symmetric logarithmic derivative (SLD) Fisher information of output states exported from the lossy channels we obtain that if we take the equal probability Schr\"{o}dinger cat states as the bases of input states the maximally entangled inputs are not optimal, however if the bases of the input states are not the equal probability Schr\"{o}dinger cat states the maximally entangled input states may be optimal for the estimating composite lossy channel.