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The optimal cloning of quantum coherent states is non-Gaussian

N.J. Cerf, O. Krueger, P. Navez, R.F. Werner, M.M. Wolf

Phys. Rev. Lett. 95, 070501 **, (2005)

DOI: 10.1103/PhysRevLett.95.070501 Pfeil
*arXiv.org*: quant-ph/0410058 Pfeil

Abstract: We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. Both optimal fidelities are attained for phase space translation covariant cloners. Remarkably, the joint fidelity is maximized by a Gaussian cloner, whereas the single-clone fidelity can be enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can achieve a single-clone fidelity of approximately 0.6826, perceivably higher than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can be realized by means of an optical parametric amplifier supplemented with a particular source of non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.