Optimal Gaussian N-to-M cloning with linear optics and Gaussian cloning of known-phase coherent states

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We show how to implement the optimal Gaussian N-to-M cloning with linear optics and homodyne detection. We also show that the Gaussian N-to-M cloning of known-phase coherent states can be performed with the fidelity √ 2 M N/2M N+M -N by linear optics and homodyne detection, and with 2√1+1/N+√ 1-1/M by utilizing quadrature squeezing. From the classical limit of the cloning (1-to-∞ cloning), a necessary condition of continuous variable quantum key distribution using known-phase coherent states is provided.