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arXiv · 1608.07983

Data processing for qubit state tomography: An information geometric approach

Akio Fujiwara·Koichi Yamagata
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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.

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Akio Fujiwara, Koichi Yamagata. 2016-08-29. Data processing for qubit state tomography: An information geometric approach. https://arxiv.org/abs/1608.07983

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