Estimation of a generalized amplitude-damping channel

The problem of finding the optimal strategy for estimating a generalized amplitude damping channel Gamma(eta)((p)) by means of the extension idxGamma(eta)((p)) is addressed. We first evaluate the quantum Fisher information of output states based on the symmetric logarithmic derivative and specify all pure-state inputs that maximize the quantum Fisher information. We next investigate the del(e) autoparallelity of output state manifolds and characterize the condition for the existence of an efficient estimator. A comparison of these results concludes that, while there is no uniformly optimal input for all p and eta, a maximally entangled input is an admissible one under a nonasymptotic setting.