Entropic Equivalence Of Measurements

In the paper, we investigate the notion of equivalence of measurements defined by means of their Shannon’s or Rényi’s entropies. As it turns out, this equivalence is quite strong and, in the most relevant case, amounts either to one measurement being a permutation of the other or to one measurement being a linear combination, given by an orthogonal matrix, of the other. In general, equivalence of measurements implies that the elements of one are scalar multiplies of elements of the other.