Quantum error precompensation for quantum noisy channels

Most previous efforts on quantum error correction focused on either extending classical error-correction schemes to the quantum regime by performing a perfect correction on a subset of errors or seeking a recovery operation to maximize the fidelity between an input state and its corresponding output state of a noisy channel. There are few results concerning quantum error precompensation. Here we design an error-precompensated input state for an arbitrary quantum noisy channel and a given target output state. By following a procedure, the required input state, if it exists, can be analytically obtained in single-partite systems. Furthermore, we also present semidefinite programs to numerically obtain the error-precompensated input states with maximal fidelities between the target state and the output state. The numerical results coincide with the analytical results.