In this paper, we first provide an inductive construction of designs on compact groups G from
those on subgroups K when (G, K) is a Gelfand pair. We then use the construction to provide
explicit constructions of unitary t-designs in the unitary group U (d) for all t and d. To the best
of our knowledge, the explicit constructions were so far known only for very special cases.
Here, explicit construction means that the entries of the unitary matrices are given by the
values of elementary functions at the root of given polynomials. We will compare our …

Explicit construction of exact unitary designs | CiNii Research … Explicit construction of
exact unitary designs … タイトル Explicit construction of exact unitary designs …