Optimal multicopy asymmetric Gaussian cloning of coherent states
Jaromı́r Fiurášek, Nicolas J. Cerf · Physical Review A · 2007
We investigate the asymmetric Gaussian cloning of coherent states which produces $M$ copies from $N$ input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.