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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
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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.

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N. J. Cerf, O. Krueger, P. Navez, R. F. Werner, M. M. Wolf. 2004-12-13. The optimal cloning of quantum coherent states is non-Gaussian. https://doi.org/10.1103/physrevlett.95.070501

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