  We propose a bio-inspired sequential quantum protocol for the cloning and
preservation of the statistics associated to quantum observables of a given
system. It combines the cloning of a set of commuting observables, permitted by
the no-cloning and no-broadcasting theorems, with a controllable propagation of
the initial state coherences to the subsequent generations. The protocol mimics
the scenario in which an individual in an unknown quantum state copies and
propagates its quantum information into an environment of blank qubits.
Finally, we propose a realistic experimental implementation of this protocol in
trapped ions.
