Suppose that a d
-dimensional Hilbert space
admits a full set of mutually unbiased bases
. A randomized quantum state tomography is a scheme for estimating an unknown quantum state on
through iterative applications of measurements
, where the numbers of applications of these measurements are random variables. We show that the space of the resulting probability distributions enjoys a mutually orthogonal dualistic foliation structure, which provides us with a simple geometrical insight into the maximum likelihood method for the quantum state tomography.
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