Probabilistic reversing operation with fidelity and purity gain for macroscopic quantum superposition

It is shown that a large class of weak disturbances on macroscopic quantum superpositions can be canceled by a probabilistic reversing operation on the system. We illustrate this for spin systems undergoing an Ising-type interaction with the environment and demonstrate that both the fidelity to the original state and the purity of the amended state can simultaneously be increased by the reversing operation. A possible experimental scheme to implement our scheme is discussed.