Information Geometry of Randomized Quantum State Tomography.

Suppose that a d-dimensional Hilbert space admits a full set of mutually unbiased bases , where . 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.