Designing the optimal quantum cloning machine for qubit case

Xiaohua Wu, Wu, Fei

Following the work of Niu and Griffiths, in \emph{Phys.Rev.A 58, 4377(1998)}, we shall investigate the problem, how to design the optimal quantum cloning machines (QCMs) for qubit system, with the help of Bloch-sphere representation. In stead of the quality factor there, the Fiuráusek's optimal condition, where the optimal cloning machine should maximize a convex mixture of the average fidelity, is used as the optimality criterion in present protocol. Almost all of the known optimal QCMs in previous works, the cloning for states with fixed polar angle, the phase-covariant cloning, the universal QCMs, the cloning for two arbitrary pure states, and the mirror phase-covariant cloning, should be discussed in a systematic way. The known results, the optimal fidelities for various input ensembles according to different optimality criteria, are recovered here. Our present scheme also offers a general way of constructing the unitary transformation to realize the optimal cloning.

Vladimír Bužek, Mark S. Hillery

Yang Shuai, Meisheng Zhao, Nai-Le Liu +1 more

We present a series of universal quantum cloning machines for two identical mixed qubits. Every machine is optimal in the sense that it achieves the optimal bound of the single copy shrinking factor. Unlike in the case of pure state cloning, the single copy shrinking factor does not uniquely determine the cloning map in the case of mixed state cloning.

Heng Fan, Yi-Nan Wang, Li Jing +4 more

Go Kato

A universal cloning machine is derived. The machine produces $c$ clones of an unknown qubit from $s$ identical replicas of qubit and $k$ identical replicas of its orthogonal qubit. For the standard cloning machine, i.e., $k=0$, the universal-not machine, $s=0$, and some other cases, the optimum machine is well known. The universal cloning machine derived in this paper gives clones whose fidelity is the same value as that for the optimum machine. In the case of sufficiently large $c$, we show that the clone fidelity generated by the cloning machine from $s\ensuremath{\ne}0$ replicas and $k\ensuremath{\ne}0$ orthogonal replicas is higher than that generated by the optimal cloning machine from $s+k$ replicas in case $s+k\ensuremath{\le}300$.

姜明明, 郁司夏