Temporal quantum tomography with weak measurements

Quantum tomography consists of the characterization of quantum states and processes from experimental measurements. If no prior knowledge of the state exists, tomography requires measurements from multiple samples. However, tomography for a quantum system with temporal processing is a fundamentally different problem. The problem is ill-posed and information about the state is lost due to the decoherence. We can still learn the properties of our input state and the dynamics under the appropriate setting. We use weak measurement history to predict the initial state of the measured quantum system. Unlike projective measurements, weak measurements make small stochastic changes to the system while giving a signal about the quantum state allowing for continuous monitoring. We also learn the dynamics of the system by learning the Kraus operators corresponding to the dynamics. By doing both, we lay out the procedure to separate the non-trivial dynamics from that caused by measurements, thus working towards quantum systems identification, and ultimately, towards adaptive quantum control.