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arXiv:quant-ph/9910048 · Physical Review Letters

Optimal Quantum Cloning via Stimulated Emission

Christoph Simon, Gregor Weihs, Anton Zeilinger

Published Mar 27, 2000• 166 citations
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Abstract

We show that optimal universal quantum cloning can be realized via stimulated emission. Universality of the cloning procedure is achieved by choosing systems that have appropriate symmetries. We first discuss a scheme based on stimulated emission in certain three-level systems, e.g., atoms in a cavity. Then we present a way of realizing optimal universal cloning based on stimulated parametric down-conversion. This scheme also implements the optimal universal NOT operation.

DOI
10.1103/physrevlett.84.2993

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We show that optimal universal quantum cloning can be realized via stimulated emission. Universality of the cloning procedure is achieved by choosing systems that have appropriate symmetries. We first discuss a scheme based on stimulated emission in certain three-level systems, e.g., atoms in a cavity. Then we present a way of realizing optimal universal cloning based on stimulated parametric down-conversion. This scheme also implements the optimal universal NOT operation.
We present ways of realizing quantum cloning via stimulated emission. Universality of the cloning procedure is achieved by choosing systems that have appropriate symmetries. We first discuss a scheme based on certain three-level systems, e.g. atoms in a cavity. Our numerical results show that this scheme approaches optimal cloning for short interaction times. Then we demonstrate that optimal universal cloning can be realized using parametric down-conversion. At the same time, our down-conversion scheme also implements the optimal universal NOT operation. We conclude with some remarks on cloning and superluminal signalling, using our cloner as an illustrative example.
Although perfect copying of unknown quantum systems is forbidden by the laws of quantum mechanics, approximate cloning is possible. A natural way of realizing quantum cloning of photons is by stimulated emission. In this context, the fundamental quantum limit to the quality of the clones is imposed by the unavoidable presence of spontaneous emission. In our experiment, a single input photon stimulates the emission of additional photons from a source on the basis of parametric down-conversion. This leads to the production of quantum clones with near-optimal fidelity. We also demonstrate universality of the copying procedure by showing that the same fidelity is achieved for arbitrary input states.
We show that optimal universal cloning of the polarization state of photons can be achieved via stimulated emission in three-level systems, both of the \ensuremath{\Lambda} and the VVV type. We establish the equivalence of our systems with coupled harmonic oscillators, which permits us to analyze the structure of the cloning transformations realized. These transformations are shown to be equivalent to the optimal cloning transformations for qubits discovered by Bu\ifmmode \check{z}\else \v{z}\fi{}ek and Hillery and Gisin and Massar. The down-conversion cloner discovered previously by some of the authors is obtained as a limiting case. We demonstrate an interesting equivalence between systems of \ensuremath{\Lambda} atoms and systems of pairwise entangled V atoms. Finally we discuss the physical differences between our photon cloners and the qubit cloners considered previously and prove that the bounds on the fidelity of the clones derived for qubits also apply in our situation.