Data processing for qubit state tomography: An information geometric approach

Abstract

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 $({\xi }_1,{\xi }_2,{\xi }_3)$ that specify qubit states should be regarded as a Riemannian manifold endowed with a metric $g_{ij}:={\delta }_{ij}/(1-({\xi }_i{)}^2)$, 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.

References in corpus (1)

• Choice of Measurement Sets in Qubit Tomography