We develop a microscopic theory for biasing the quantum trajectories of an open quantum system, which renders rare trajectories typical. To this end we consider a discrete-time quantum dynamics, where the open system collides sequentially with qubit probes which are then measured. A theoretical framework is built in terms of thermodynamic functionals in order to characterize its quantum trajectories (each embodied by a sequence of measurement outcomes). We show that the desired biasing is achieved by suitably modifying the Kraus operators describing the discrete open system dynamics. From a microscopical viewpoint and for short collision times, this corresponds to adding extra collisions which enforce the system to follow a desired rare trajectory. The above extends the theory of biased quantum trajectories from Lindblad-like dynamics to sequences of arbitrary dynamical maps, providing at once a transparent physical interpretation.

我们开发了一种用于偏置开放量子系统的量子轨迹的微观理论，这使得罕见的轨迹具有典型性。为此，我们考虑离散时间量子动力学，其中开放系统依次与量子位探针碰撞，然后对其进行测量。根据热力学泛函建立理论框架，以表征其量子轨迹（每个轨迹由一系列测量结果体现）。我们表明通过适当修改描述离散开放系统动力学的克劳斯算子来实现所需的偏置。从微观角度来看，对于较短的碰撞时间，这对应于添加额外的碰撞，强制系统遵循所需的罕见轨迹。