  We investigate a range of methods to perform tomography in a solid-state
qubit device, for which a priori initialization and measurement of the qubit is
restricted to a single basis of the Bloch sphere. We explore and compare
several methods to acquire precise descriptions of additional states and
measurements, quantifying both stochastic and systematic errors, ultimately
leading to a tomographically-complete set that can be subsequently used in
process tomography. We focus in detail on the example of a spin qubit formed by
the singlet-triplet subspace of two electron spins in a GaAs double quantum
dot, although our approach is quite general.
