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Chinese Physics B

A quantum network for implementation of the optimal quantum cloning

Dai Jie-lin, Wen‐Hai Zhang

Published Feb 1, 2009• 10 citations
Publisher

Abstract

This paper presents a quantum network to implement the optimal 1 → 2 quantum cloning in 2 dimensions, including the optimal asymmetric universal, the optimal symmetric phase-covariant, and the asymmetric real state cloning. By only choosing different angles of the single-qubit rotations, the quantum network can implement three optimal quantum cloning.

DOI
10.1088/1674-1056/18/2/008

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This paper presents a quantum network to implement the optimal 1 → 2 quantum cloning in 2 dimensions, including the optimal asymmetric universal, the optimal symmetric phase-covariant, and the asymmetric real state cloning. By only choosing different angles of the single-qubit rotations, the quantum network can implement three optimal quantum cloning.
While exact cloning of an unknown quantum state is prohibited by the linearity of quantum mechanics, approximate cloning is possible and has been used, e.g., to derive limits on the security of quantum communication protocols. In the case of asymmetric cloning, the information from the input state is distributed asymmetrically between the different output states. Here, we consider asymmetric phase-covariant cloning, where the goal is to optimally transfer the phase information from a single input qubit to different output qubits. We construct an optimal quantum cloning machine for two qubits that does not require ancilla qubits and implement it on an NMR quantum information processor.
In this paper we demonstrate that optimal $1\ensuremath{\rightarrow}M$ phase-covariant cloning quantum cloning is available via free dynamical evolution of spin networks. By properly designing the network and the couplings between spins, we show that optimal $1\ensuremath{\rightarrow}M$ phase-covariant cloning can be achieved if the initial state is prepared as a specific symmetric state. Especially, when MMM is an odd number, the optimal phase-covariant cloning can be achieved without ancillas. Moreover, we demonstrate that the same framework is capable for optimal $1\ensuremath{\rightarrow}2$ universal cloning.
We propose an experimentally unified linear optical scheme to implement the optimal symmetric one to two (1 → 2) universal, optimal symmetric 1 → 2 phase-covariant and optimal symmetric economical one to three (1 → 3) phase-covariant quantum cloning machines of the polarization state of the single photon. This scheme requires single-photon sources as the input state. Here, we use a laser beam attenuated to the single-photon level as the input source. The scheme relies on one polarized qubit and two location qubits and it also involves linear optical elements. It is shown that under certain conditions, the scheme is feasible by current experimental technology.