Prediction and retrodiction for a continuously monitored superconducting qubit

The quantum state of a superconducting transmon qubit inside a three-dimensional cavity is monitored by reflection of a microwave field on the cavity. The information inferred from the measurement record is incorporated in a density matrix ρt, which is conditioned on probe results until t, and in an auxiliary matrix Et, which is conditioned on probe results obtained after t. Here, we obtain these matrices from experimental data and we illustrate their application to predict and retrodict the outcome of weak and strong qubit measurements.