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The article undertakes the problem of pure state estimation from projectivemeasurements based on photon counting. Two generic frames for qubit tomographyare considered -- one composed of the elements of the SIC-POVM and the otherdefined by the vectors from the mutually unbiased bases (MUBs). Both frames arecombined with the method of least squares in order to reconstruct a sample ofinput qubits with imperfect measurements. The accuracy of each frame isquantified by the average fidelity and purity. The efficiency of the frames iscompared and discussed. The method can be generalized to higher-dimensionalstates and transferred to other fields where the problem of complex vectorsreconstruction appears.

Quantum Tomography of Pure States with Projective Measurements Distorted by Experimental Noise