Integrated quantum photonic circuits are becoming increasingly complex.
Accurate calibration of device parameters and detailed characterization of the
prepared quantum states are critically important for future progress. Here we
report on an effective experimental calibration method based on Bayesian
updating and Markov chain Monte Carlo integration. We use this calibration
technique to characterize a two qubit chip and extract the reflectivities of
its directional couplers. An average quantum state tomography fidelity of
93.79+/-1.05% against the four Bell states is achieved. Furthermore, comparing
the measured density matrices against a model using the non-ideal device
parameters derived from the calibration we achieve an average fidelity of
97.57+/-0.96%. This pinpoints non-ideality of chip parameters as a major factor
in the decrease of Bell state fidelity. We also perform quantum state
tomography for Bell states while continuously varying photon distinguishability
and find excellent agreement with theory
