  The effectiveness of measurement-based feedback control (MBFC) protocols is
hampered by the presence of measurement noise, which affects the ability to
accurately infer the underlying dynamics of a quantum system from noisy
continuous measurement records to determine an accurate control strategy. To
circumvent such limitations, this work explores a real-time stochastic state
estimation approach that enables noise-free monitoring of the conditional
dynamics including the full density matrix of the quantum system using noisy
measurement records within a single quantum trajectory -- a method we name as
`conditional state tomography'. This, in turn, enables the development of
precise MBFC strategies that lead to effective control of quantum systems by
essentially mitigating the constraints imposed by measurement noise and has
potential applications in various feedback quantum control scenarios. This
approach is particularly useful for reinforcement-learning (RL)-based control,
where the RL-agent can be trained with arbitrary conditional averages of
observables, and/or the full density matrix as input (observation), to quickly
and accurately learn control strategies.
