  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.
