Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language study variety of areas. Remarkably, one the key information-theoretic quantities is given by relative entropy, which quantifies how difficult tell apart two probability distribut...

Let G be a group of order mu and U a normal subgroup of G of order u. Let G/U = {U1, U2, · · · , Um} be the set of cosets of U in G. We say a matrix H = [hij ] order k with entries from G is a quasi-generalized Hadamard matrix with respect to the cosets G/U if ∑ 1≤t≤k hith −1 jt = λij1U1 + · · · + λijmUm (∃λij1, · · · , ∃λijm ∈ Z) for any i ̸= j. On the other hand, in our previous article we def...