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arXiv:quant-ph/0510147 · Physical Review A

Optimal quantum cloning via spin networks

Qing Chen, Jianhua Cheng, Ke-Lin Wang, Jiangfeng Du

Published Sep 18, 2006• 21 citations
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Abstract

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 $M$ 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.

DOI
10.1103/physreva.74.034303

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In this paper we demonstrate that optimal 1\ensuremath→M1\ensuremath{\rightarrow}M1\ensuremath→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→M1\ensuremath{\rightarrow}M1\ensuremath→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→21\ensuremath{\rightarrow}21\ensuremath→2 universal cloning.
In this paper we present an approach to quantum cloning with unmodulated spin networks. The cloner is realized by a proper design of the network and a choice of the coupling between the qubits. We show that in the case of phase covariant cloner the XYXYXY coupling gives the best results. In the $1\ensuremath{\rightarrow}2$ cloning we find that the value for the fidelity of the optimal cloner is achieved, and values comparable to the optimal ones in the general $N\ensuremath{\rightarrow}M$ case can be attained. If a suitable set of network symmetries are satisfied, the output fidelity of the clones does not depend on the specific choice of the graph. We show that spin network cloning is robust against the presence of static imperfections. Moreover, in the presence of noise, it outperforms the conventional approach. In this case the fidelity exceeds the corresponding value obtained by quantum gates even for a very small amount of noise. Furthermore, we show how to use this method to clone qutrits and qudits. By means of the Heisenberg coupling it is also possible to implement the universal cloner although in this case the fidelity is 10% off that of the optimal cloner.
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We introduce an approach to quantum cloning based on spin networks and we demonstrate that phase covariant cloning can be realized using no external control but only with a proper design of the Hamiltonian of the system. In the $1\ensuremath{\rightarrow}2$ cloning we find that the XYXYXY model saturates the value for the fidelity of the optimal cloner and gives values comparable to it in the general $N\ensuremath{\rightarrow}M$ case. We finally discuss the effect of external noise. Our protocol is much more robust to decoherence than a conventional procedure based on quantum gates.
We present a scheme which transforms a one-input qubit to MMM identical copies with optimal fidelity via free dynamical evolution of spin star networks. We demonstrate that the Heisenberg XXZXXZXXZ coupling can meet the challenge. The initial state of the copying machine and the parameters of the spin Hamiltonian are discussed in detail. Furthermore we have proposed a feasible method to prepare the initial state of the copying machine.