Two-qubit state recovery from amplitude damping based on weak measurement

In this paper, we propose a feed-forward control approach to protect arbitrary two-qubit pure and mixed initial states using the weak measurement. A feed-forward operation and measurements are used before the noise channel, and afterward, a reversed operation and measurements are applied to recover the state back to its initial state. In the case of two-qubit pure states, we use the unraveling trick to describe the state of the system in each step of the control procedure. For two-qubit mixed states, a completely positive trace-preserving map is implemented. Finally, the fidelity and success probability are used to evaluate the effect of protection. The complete recovery conditions for the measurement strengths are derived, under which we achieve the optimal fidelity and the success probability of recovering the initial pure and mixed states.