ON A SYSTEM OF MEASUREMENTS WHICH IS COMPLETE IN A STATISTICAL SENSE
Andrzej Komisarski, Adam Paszkiewicz · Infinite Dimensional Analysis Quantum Probability and Related Topics · 2013
We show that if H = ℂd then there exists a system of d + 1 measurements which allows to recover an unknown state ρ on H from the probabilities of results of these measurements. Moreover, we show that a randomly chosen system of d + 1 measurements has the above property with probability 1. We also present some novel properties of known mutually unbiased bases.