Quantum information reclaiming by classical feedback from the environment

We investigate the quantum information reclaim from the environment after amplitude damping has occurred. In particular we address the question of optimal measurement on the environment to perform the best possible correction on two and three dimensional quantum systems. Depending on the dimension we show that the entanglement fidelity (the measure quantifying the correction performance) is or is not the same for all possible measurements and uncover the optimal measurement leading to the maximum entanglement fidelity. Furthermore, we study random unitary channel acting on nqubits by using the classical result of measurement on the environment of m.