Data processing for qubit state tomography: An information geometric approach

A statistically feasible data post-processing method for the conventional qubit state tomography is studied from an information geometrical point of view. It is shown that the space $(-1,1)^3$ of the Stokes parameters $(ξ_1, ξ_2,ξ_3)$ that specify qubit states should be regarded as a Riemannian manifold endowed with a metric $g_{ij}:=δ_{ij}/(1-(ξ_i)^2)$, and that the data processing based on the maximum likelihood method is realized by the orthogonal projection from the empirical distribution onto the Bloch sphere with respect to the metric $g_{ij}$. An efficient algorithm for computing the maximum likelihood estimate is also proposed.

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