Optimization of quantum state tomography in the presence of experimental constraints

In the absence of experimental constraints, optimal measurement schemes for quantum state tomography are well understood. We consider the scenario where the experimenter doesn't have arbitrary freedom to construct their measurement set, and may therefore not be able to implement a known optimal scheme. We introduce a simple procedure for minimizing the uncertainty in the reconstructed quantum state for an arbitrary tomographic scheme. We do this by defining a figure of merit based on the equally-weighted variance of the measurement statistics. This figure of merit is straightforwardly based on the singular value decomposition of the measurement matrix, making it well-suited for optimization.