Open-system quantum error correction

We study the performance of quantum error correction (QEC) on a system undergoing open-system (OS) dynamics. The noise on the system originates from a joint quantum channel on the system-bath composite, a framework that includes and interpolates between the commonly used system-only quantum noise channel model and the system-bath Hamiltonian noise model. We derive the perfect OSQEC conditions, with QEC recovery only on the system and not the inaccessible bath. When the noise is only approximately correctable, the generic case of interest, we quantify the performance of OSQEC using worst-case fidelity. We find that the leading deviation from unit fidelity after recovery is quadratic in the uncorrectable part, a result reminiscent of past work on approximate QEC for system-only noise, although the approach here requires the use of different techniques than in past work.