It is well known that classical information can be cloned, but non-orthogonal
quantum states cannot be cloned, and non-commuting quantum states cannot be
broadcast. We conceive a scenario in which the object we want to broadcast is
the statistical distinguishability, as quantified by quantum Fisher
information, about a signal parameter encoded in quantum states. We show that
quantum Fisher information cannot be cloned, whilst it might be broadcast even
when the input states are non-commuting. This situation interpolates between
cloning of classical information and no-broadcasting of quantum information,
and indicates a hybrid way of information broadcasting which is of particular
significance from both practical and theoretical perspectives.Comment: 5 pages. Improved version. Any comments is welcom
