Fig. 4

Analysis of a feedback protocol stabilizing the state \(\left|{\psi }_{{\rm{target}}}(t)\right\rangle =\exp (-i{\omega }_{0}{\sigma }_{z}t\mathrm{/2})\left|{+}_{x}\right\rangle\). Left: Trajectory in the Bloch sphere in the case of perfect feedback (green), imperfect feedback (blue) and without feedback (red). Right: Normalized distributions of quantum heat increments P _γ [δQ _q] (dashed black) and feedback work P _γ [δW _fb] (bars) performed by the feedback source \({\mathcal F}\). The work distribution P _γ [δW _fb] is defined like in Eq. 28. Top right: The two distributions match, such that the state is perfectly stabilized. Bottom right: The distribution of P _γ [δW _fb] is bounded and the feedback is not perfect. Parameters: \(\hbar = 1\), evolution time T = 1.5/ω ₀, pure dephasing rate Γ^* = 0.1ω ₀, feedback work cutoff: \({|\delta {W}_{{\rm{fb}}}|}^{{\rm{\max }}}\mathrm{=0.05} {\omega }_{0}\)