Biomimetic Cloning of Quantum Observables

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.The authors acknowledge funding from Basque Government BFI-2012-322 and IT472-10 grants, Spanish MINECO FIS2012-36673-C03-02, Ramon y Cajal Grant RYC-2012-11391, UPV/EHU UFI 11/55, CCQED, PROMISCE, and SCALEQIT European projects