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International Journal of Quantum Information

MULTICLONES QUANTUM CLONING OF QUTRITS

Wen‐Hai Zhang, Dai Jie-lin, Zhuo‐Liang Cao, Ming Yang

Published Oct 1, 2010• 0 citations
Publisher

Abstract

In this paper, we present the explicit transformations of the optimal 1 → 3 universal quantum and the phase-covariant cloning in 3 dimensions (qutrits). The fidelities of two types of cloners reach the theoretical bounds.
DOI
10.1142/s021974991000685x

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We consider cloning transformations of equatorial qubits $|{\ensuremath{\psi}}_{\ensuremath{\varphi}}〉=1/\sqrt{2}(|0〉{+e}^{i\ensuremath{\varphi}}|1〉)$ and qutrits $|{\ensuremath{\psi}}_{\ensuremath{\varphi},\ensuremath{\theta}}〉=1/\sqrt{3}(|0〉{+e}^{i\ensuremath{\varphi}}|1〉{+e}^{i\ensuremath{\theta}}|2〉),$ with the transformation covariant for rotation of the phases $\ensuremath{\varphi}$ and $\ensuremath{\theta}.$ The optimal cloning maps are derived without simplifying assumptions from first principles, for any number of input and output qubits, and for a single-input qutrit and any number of output qutrits. We also compare the cloning maps for global and single-particle fidelities, and we show that the two criteria lead to different optimal maps.