Time-reversibility in Quantum Feedback Protocols*

In open quantum systems, measurements by a probe or the environment cause backaction. While these interactions do not necessarily break time-reversal symmetry, a statistical arrow of time emerges due to the correlations between the quantum state and the measurement. Quantum feedback protocols utilize rotations to correct for quantum backaction, effectively closing the system evolution. We study time reversibility of state stabilization by examining the effectiveness of time-reversed versus time-ordered feedback protocols. We also investigate the effect of finite efficiency detection in these state stabilization protocols.