Repetition code under coherent dynamics and incoherent noise

Open quantum systems may undergo unitary evolution, dephasing by an environment, and monitoring by an observer. From the perspective of quantum error correction, these three types of evolution arise as coherent dynamics, incoherent noise, and check measurements. When the check measurements are weak (i.e. not fully projective), the corrupted phase resulting from the coherent dynamics alone may differ from that driven by incoherent noise. For example, the steady state under weak measurements and coherent dynamics can undergo a measurement-induced entanglement transition. Focusing on the steady-state dynamics of the 1d repetition code, we explore whether a "coherent-error corrupted" phase, distinct from the standard incoherent-error corrupted phase, survives in the presence of incoherent noise.